Vector solitons in nonlinear lattices (2009)
Kartashov, Yaroslav V., Malomed, Boris A., Vysloukh, Victor A., Torner, Lluis
We consider two-component solitons in a medium with a periodic modulation of the nonlinear coefficient. The modulation enables the existence of complex multihump vector states. In particular, vector...
Kartashov, Yaroslav V., Malomed, Boris A., Vysloukh, Victor A., Torner, Lluis
We address necklace solitons supported by circular waveguide arrays with out-of-phase modulation of nonlinearity and linear refractive index. Such two-dimensional necklace solitons appear as rings of...
Chen, Peter Y. P., Malomed, Boris A.
We report results of the study of solitons in a system of two nonlinear-Schrodinger (NLS) equations coupled by the XPM interaction, which models the co-propagation of two waves in metamaterials(MMs)....
Solitons and solitary vortices in "pancake"-shaped Bose-Einstein condensates (2009)
Salasnich, Luca, Malomed, Boris A.
We study fundamental and vortical solitons in disk-morphed Bose-Einstein condensates (BECs) subject to strong confinement along the axial direction. Starting from the three-dimensional (3D)...
Cuevas, J., Malomed, Boris A., Kevrekidis, P. G., Frantzeskakis, D. J.
We study families of one-dimensional matter-wave bright solitons supported by the competition of contact and dipole-dipole (DD) interactions of opposite signs. Soliton families are found, and their...
Intrinsic localized modes in parametrically-driven arrays of nonlinear resonators (2009)
Kenig, Eyal, Malomed, Boris A., Cross, M. C., Lifshitz, Ron
We study intrinsic localized modes (ILMs), or solitons, in arrays of parametrically-driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS and...
Wainblat, George, Malomed, Boris A.
We report results of systematic numerical analysis of collisions between two and three stable dissipative solitons in the two-dimensional (2D) complex Ginzburg- Landau equation (CGLE) with the...
Filatrella, Giovanni, Malomed, Boris A., Salasnich, Luca
We study suppression of the collapse and stabilization of matter-wave solitons by means of time-periodic modulation of the effective nonlinearity, using the nonpolynomial Schroedinger equation (NPSE)...
Magnetooptical control of light collapse in bulk Kerr media (2009)
Linzon, Yoav, Rutkowska, Katarzyna A., Malomed, Boris A., Morandotti, Roberto
Magneto-optical crystals allow an efficient control of the birefringence of light via the Cotton-Mouton and Faraday effects. These effects enable a unique combination of adjustable linear and...
Stable two-dimensional solitons in nonlinear lattices (2009)
Kartashov, Yaroslav V., Malomed, Boris A., Vysloukh, Victor A., Torner, Lluis
We address the existence and stability of two-dimensional solitons in optical or matter-wave media, which are supported by purely nonlinear lattices in the form of a periodic array of cylinders with...
Entanglement generation by collisions of quantum solitons (2009)
Lewenstein, Maciej, Malomed, Boris A.
We present general analytic expressions describing generation of the entanglement in collisions of initially uncorrelated quantum solitons. The results, obtained by means of the Born approximation,...
Two-component gap solitons with linear interconversion (2008)
Adhikari, Sadhan K., Malomed, Boris A.
We consider one-dimensional solitons in a binary Bose-Einstein condensate with linear coupling between the components, trapped in an optical-lattice potential. The inter-species and intra-species...
Driben, Rodislav, Malomed, Boris A.
It is known that optical-lattice (OL) potentials can stabilize solitons and solitary vortices against the critical collapse, generated by the cubic attractive nonlinearity in the 2D geometry. We...
Kartashov, Yaroslav V., Malomed, Boris A., Vysloukh, Victor A., Torner, Lluis
We introduce a new species of gap solitons (GSs) supported by an azimuthally modulated guiding ring in defocusing cubic media. The periodicity in the azimuthal direction strongly modifies properties...
Spontaneous symmetry breaking in a nonlinear double-well structure (2008)
Mayteevarunyoo, Thawatchai, Malomed, Boris A., Dong, Guangjiong
We propose a model of a nonlinear double-well potential (NDWP), alias a double-well pseudopotential, with the objective to study an alternative implementation of the spontaneous symmetry breaking...
Solitons in one-dimensional photonic crystals (2008)
Mayteevarunyoo, Thawatchai, Malomed, Boris A.
We report results of a systematic analysis of spatial solitons in the model of 1D photonic crystals, built as a periodic lattice of waveguiding channels, of width D, separated by empty channels of...
Chen, Peter Y. P., Malomed, Boris A.
The problem of the stability of solitons in second-harmonic-generating media with normal group-velocity dispersion (GVD) in the second-harmonic (SH) field, which is generic to available chi^(2)...
Gap solitons in grating superstructures (2008)
Mayteevarunyoo, Thawatchai, Malomed, Boris A.
We report results of the investigation of gap solitons (GSs) in the generic model of a periodically modulated Bragg grating (BG), which includes periodic modulation of the BG chirp or local...
Dynamics of matter-wave solitons in a time-modulated two-dimensional optical lattice (2008)
Burlak, Gennadiy, Malomed, Boris A.
By means of the variational approximation (VA) and systematic simulations, we study dynamics and stability boundaries for solitons in a two-dimensional (2D) self-attracting Bose-Einstein condensate...
Supersolitons: Solitonic excitations in atomic soliton chains (2008)
Novoa, David, Malomed, Boris A., Michinel, Humberto, Perez-Garcia, Victor M.
We show that, by appropriately tuning physically relevant interactions in two-component nonlinear Schrodinger equations, it is possible to achieve a regime with particle-like solitonic collisions....
Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity (2008)
Birnbaum, Ze'ev, Malomed, Boris A.
We present eight types of spatial optical solitons which are possible in a model of a planar waveguide that includes a dual-channel trapping structure and competing (cubic-quintic) nonlinearity....
Symbiotic gap and semi-gap solitons in Bose-Einstein condensates (2008)
Adhikari, Sadhan K., Malomed, Boris A.
Using the variational approximation and numerical simulations, we study one-dimensional gap solitons in a binary Bose-Einstein condensate trapped in an optical-lattice potential. We consider the case...
Gap solitons in superfluid boson-fermion mixtures (2007)
Adhikari, Sadhan K., Malomed, Boris A.
Using coupled equations for the bosonic and fermionic order parameters, we construct families of gap solitons (GSs) in a nearly one-dimensional Bose-Fermi mixture trapped in a periodic...
Fusion of necklace-ring patterns into vortex and fundamental solitons in dissipative media (2007)
He, Y. J., Malomed, Boris A., Wang, H. Z.
We demonstrate that necklace-shaped arrays of localized spatial beams can merge into stable fundamental or vortex solitons in a generic model of laser cavities, based on the two-dimensional complex...
Self--Guided Beams in a Diffractive (2007)
Medium Variational, Victoria V. Steblina, Yuri S. Kivshar, Mietek Lisak, Boris A. Malomed
It is demonstrated that the (1+1)- and (2+1)-dimensional self--guided beams (two-wave parametric spatial solitons) in a diffractive dielectric medium with purely quadratic nonlinearity (the...
Moving Embedded Solitons (2007)
Alan R Champneys, Boris A Malomed
. The first theoretical results are reported predicting moving solitons residing inside (embedded into) the continuous spectrum of radiation modes. The model taken is a Bragggrating medium with Kerr...
Department of Mathematical Sciences, Loughborough University, (2007)
Roger Grimshaw, Boris A. Malomed, Georg A. Gottwald
A general model is introduced to describe a wave-envelope system for the situation when the linear dispersion relation has three branches, which in the absence of any coupling terms between these...
Natalia L. Komarova, Boris A. Malomed, J. V. Moloney, Alan C. Newell
Starting from the Maxwell-Bloch equations for a 3D ring-cavity laser, we analyze stability of the nonlasing state and demonstrate that, at the instability threshold, the wave vectors of the critical...
\Dispersion management " for solitons in a Korteweg-de Vries system (2007)
Simon Clarke, Boris A. Malomed, Roger Grimshaw
The variable-coe cient Korteweg-de Vries is used to present a basic model, which has the form of a Korteweg-de Vries equation with a periodically varying third-order dispersion coe cient, that can...
Matter-wave vortices in cigar-shaped and toroidal waveguides (2007)
Salasnich, Luca, Toigo, Flavio, Malomed, Boris A.
We study vortical states in a Bose-Einstein condensate (BEC) filling a cigar-shaped trap. An effective one-dimensional (1D) nonpolynomial Schroedinger equation (NPSE) is derived in this setting, for...
Matuszewski, Michal, Malomed, Boris A., Trippenbach, Marek
We consider effects of inter-species attraction on two-component gap solitons (GSs) in the binary BEC with intra-species repulsion, trapped in the one-dimensional optical lattice (OL). Systematic...
Gubeskys, Arthur, Malomed, Boris A.
Models of two-dimensional (2D) traps, with the double-well structure in the third direction, for Bose-Einstein condensate (BEC) are introduced, with attractive or repulsive interactions between...
Guiding-center solitons in rotating potentials (2007)
Kartashov, Yaroslav V., Malomed, Boris A., Torner, Lluis
We demonstrate that rotating quasi-one-dimensional potentials, periodic or parabolic, support solitons in settings where they are otherwise impossible. Ground-state and vortex solitons are found in...
Modulated amplitude waves in collisionally inhomogeneous Bose–Einstein condensates (2007)
Porter, Mason A., Kevrekidis, P. G., Malomed, Boris A., Frantzeskakis, D. J.
We investigate the dynamics of an effectively one-dimensional Bose–Einstein condensate (BEC) with scattering length a subjected to a spatially periodic modulation, a=a(x)=a(x+L). This...
Optoacoustic solitons in Bragg gratings (2007)
Tasgal, Richard S., Band, Y. B., Malomed, Boris A.
Optical gap solitons, which exist due to a balance of nonlinearity and dispersion due to a Bragg grating, can couple to acoustic waves through electrostriction. This gives rise to a new species of...
Gubeskys, Arthur, Malomed, Boris A.
We study spontaneous symmetry breaking in a system of two parallel quasi-one-dimensional traps, equipped with optical lattices (OLs) and filled with a Bose-Einstein condensate (BEC). The cores are...
Interactions of solitons with complex defects in Bragg gratings (2007)
Chen, Peter Y P, Malomed, Boris A, Chu, Pak L
We examine collisions of moving solitons in a fiber Bragg grating with a triplet composed of two closely set repulsive defects of the grating and an attractive one inserted between them. A doublet...
Three-dimensional vortex solitons in self-defocusing media (2007)
Efremidis, Nikolaos K., Hizanidis, Kyriakos, Malomed, Boris A., Di Trapani, Paolo
We demonstrate that families of vortex solitons are possible in a bi-dispersive three-dimensional nonlinear Schrodinger equation. These solutions can be considered as extensions of two-dimensional...
Albuch, Lior, Malomed, Boris A.
It is well known that a symmetric soliton in coupled nonlinear Schroedinger (NLS) equations with the cubic nonlinearity loses its stability with the increase of its energy, featuring a transition...
Miscibility in a degenerate fermionic mixture induced by linear coupling (2006)
Adhikari, Sadhan K., Malomed, Boris A.
We consider a one-dimensional mean-field-hydrodynamic model of a two-component degenerate Fermi gas in an external trap, each component representing a spin state of the same atom. We demonstrate that...
Vector solitons in nearly-one-dimensional Bose-Einstein condensates (2006)
Salasnich, Luca, Malomed, Boris A.
We derive a system of nonpolynomial Schroedinger equations (NPSEs) for one-dimensional wave functions of two components in a binary self-attractive Bose-Einstein condensate loaded in a cigar-shaped...
Partially incoherent gap solitons in Bose-Einstein condensates (2006)
Merhasin, I. M., Malomed, Boris A., Band, Y. B.
We construct families of incoherent matter-wave solitons in a repulsive degenerate Bose gas trapped in an optical lattice (OL), i.e., gap solitons, and investigate their stability at zero and finite...
De Nicola, Sergio, Malomed, Boris A., Fedele, Renato
We demonstrate that a tight transverse trap with the local frequency, $% \omega_{\perp}$, gradually varying in the longitudinal direction ($x$) induces an effective potential for one-dimensional...
Modulated Amplitude Waves in Collisionally Inhomogeneous Bose-Einstein Condensates (2006)
Porter, Mason A., Kevrekidis, P. G., Malomed, Boris A., Frantzeskakis, D. J.
We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length $a$ subjected to a spatially periodic modulation, $a=a(x)=a(x+L)$. This...
Gap solitons in quasiperiodic optical lattices (2006)
Sakaguchi, Hidetsugu, Malomed, Boris A.
Families of solitons in one- and two-dimensional (1D and 2D) Gross-Pitaevskii equations with the repulsive nonlinearity and a potential of the quasicrystallic type are constructed (in the 2D case,...
Mobility of Discrete Solitons in Quadratically Nonlinear Media (2006)
Susanto, H., Kevrekidis, P. G., Carretero-Gonzalez, R., Malomed, Boris A., Frantzeskakis, D. J.
We study the mobility of solitons in second-harmonic-generating lattices. Contrary to what is known for their cubic counterparts, discrete quadratic solitons are mobile not only in the...
Stable circulation modes in a dual-core matter-wave soliton laser (2006)
Chen, Peter Y. P., Malomed, Boris A.
We consider a model of a matter-wave laser generating a periodic array of solitary-wave pulses. The system, a general version of which was recently proposed in Ref. [5], is composed of two parallel...
Matter-wave solitons in radially periodic potentials (2006)
Baizakov, Bakhtiyor B., Malomed, Boris A., Salerno, Mario
We investigate two-dimensional (2D) states of Bose-Einstein condensates (BEC) with self-attraction or self-repulsion, trapped in an axially symmetric optical-lattice potential periodic along the...
All-optical switching in a two-channel waveguide with cubic-quintic nonlinearity (2006)
Driben, Rodislav, Malomed, Boris A, Chu, Pak L
We consider dynamics of spatial beams in a dual-channel waveguide with competing cubic and quintic (CQ) nonlinearities. Gradually increasing the power in the input channel, we identify four different...
Khaykovich, Lev, Malomed, Boris A.
By means of analytical and numerical methods, we study how the residual three-dimensionality affects dynamics of solitons in an attractive Bose-Einstein condensate loaded into a cigar-shaped trap....
Vortex stability in nearly two-dimensional Bose-Einstein condensates with attraction (2006)
Mihalache, Dumitru, Mazilu, Dumitru, Malomed, Boris A., Lederer, Falk
We perform accurate investigation of stability of localized vortices in an effectively two-dimensional ("pancake-shaped") trapped BEC with negative scattering length. The analysis combines...
Li, Lu, Li, Zaidong, Malomed, Boris A., Mihalache, Dumitru, Liu, W. M.
We find one-, two-, and three-component solitons of the polar and ferromagnetic (FM) types in the general (non-integrable) model of a spinor (three-component) model of the Bose-Einstein condensate...
Two-dimensional solitons in saturable media with a quasi-one-dimensional lattice potential (2006)
Mayteevarunyoo, Thawatchai, Malomed, Boris A.
We study families of solitons in a two-dimensional (2D) model of the light transmission through a photorefractive medium equipped with a (quasi-)one-dimensional photonic lattice. The soliton families...
Semi-discrete composite solitons in arrays of quadratically nonlinear waveguides (2006)
Panoiu, Nicolae C., Osgood, Richard M., Malomed, Boris A.
We demonstrate that an array of discrete waveguides on a slab substrate, both featuring the $\chi^{2}$ nonlinearity, supports stable solitons composed of discrete and continuous components. Two...
Sakaguchi, Hidetsugu, Malomed, Boris A.
We introduce a dynamical model of a Bose-Einstein condensate based on the 2D Gross-Pitaevskii equation, in which the nonlinear coefficient is a function of radius. The model describes a situation...
Multipole-mode solitons in Bessel optical lattices (2005)
Kartashov, Yaroslav V., Carretero-Gonzalez, R., Malomed, Boris A., Vysloukh, Victor A., Torner, Lluis
We study basic properties of quiescent and rotating multipole-mode solitons supported by axially symmetric Bessel lattices in a medium with defocusing cubic nonlinearity. The solitons can be found in...
Alternate solitons: Nonlinearly-managed one- and two-dimensional solitons in optical lattices (2005)
Gubeskys, Arthur, Malomed, Boris A., Merhasin, Ilya M.
We consider a model of Bose-Einstein condensates which combines a stationary optical lattice (OL) and periodic change of the sign of the scattering length (SL) due to the Feshbach-resonance...
Multidimensional semi-gap solitons in a periodic potential (2005)
Baizakov, Bakhtiyor B., Malomed, Boris A., Salerno, Mario
The existence, stability and other dynamical properties of a new type of multi-dimensional (2D or 3D) solitons supported by a transverse low-dimensional (1D or 2D, respectively) periodic potential in...
A model of a dual-core matter-wave soliton laser (2005)
Chen, Peter Y. P., Malomed, Boris A.
We propose a system which can generate a periodic array of solitary-wave pulses from a finite reservoir of coherent Bose-Einstein condensate (BEC). The system is built as a set of two parallel...
Discrete embedded solitons (2005)
Yagasaki, Kazuyuki, Champneys, Alan R., Malomed, Boris A.
We address the existence and properties of discrete embedded solitons (ESs), i.e., localized waves existing inside the phonon band in a nonlinear dynamical-lattice model. The model describes a...
Photon-number fluctuation and correlation of bound soliton pairs in mode-locked fiber lasers (2005)
Lee, Ray-Kuang, Lai, Yinchieh, Malomed, Boris A.
Quantum photon-number fluctuation and correlation of bound soliton pairs in mode-locked fiber lasers are studied based on the complex Ginzburg-Landau equation model. We find that, depending on their...
Motion of discrete solitons assisted by nonlinearity management (2004)
Cuevas, Jesus, Malomed, Boris A., Kevrekidis, Panayotis G.
We demonstrate that periodic modulation of the nonlinearity coefficient in the discrete nonlinear Schr\"{o}dinger (DNLS) equation can strongly facilitate creation of traveling solitons in the...
Coupled-mode theory for spatial gap solitons in optically-induced lattices (2004)
Malomed, Boris A., Ostrovskaya, Elena A., Kivshar, Yuri S.
We develop a coupled-mode theory for spatial gap solitons in the one-dimensional photonic lattices induced by interfering optical beams in a nonlinear photorefractive crystal. We derive a novel...
Optical-parametric-oscillator solitons driven by the third harmonic (2004)
Lutsky, Vitaly, Malomed, Boris A.
We introduce a model of a lossy second-harmonic-generating (chi^2) cavity externally pumped at the third harmonic, which gives rise to driving terms of a new type, corresponding to a cross-parametric...
Resonant nonlinearity management for nonlinear-Schr\"{o}dinger solitons (2004)
Sakaguchi, Hidetsugu, Malomed, Boris A.
We consider effects of a periodic modulation of the nonlinearity coefficient on fundamental and higher-order solitons in the one-dimensional NLS equation, which is an issue of direct interest to...
Gap solitons in a model of a hollow optical fiber (2004)
Merhasin, I. M., Malomed, Boris A.
We introduce a models for two coupled waves propagating in a hollow-core fiber: a linear dispersionless core mode, and a dispersive nonlinear quasi-surface one. The linear coupling between them may...
Chen, Yi-Fan, Beckwitt, Kale, Wise, Frank W., Malomed, Boris A.
Criteria for experimental observation of multi-dimensional optical solitons in media with saturable refractive nonlinearities are developed. The criteria are applied to actual material parameters...
Nonlinear Lattice Dynamics of Bose-Einstein Condensates (2004)
Porter, Mason A., Carretero-González, R., Kevrekidis, P. G., Malomed, Boris A.
The Fermi-Pasta-Ulam (FPU) model, which was proposed 50 years ago to examine thermalization in non-metallic solids and develop ``experimental'' techniques for studying nonlinear problems, continues...
Static and rotating domain-wall crosses in Bose-Einstein condensates (2004)
Malomed, Boris A., Nistazakis, H. E., Frantzeskakis, D. J., Kevrekidis, P. G.
For a Bose-Einstein condensate (BEC) in a two-dimensional (2D) trap, we introduce cross patterns, which are generated by intersection of two domain walls (DWs) separating immiscible species, with...
Rapti, Z., Trombettoni, A., Kevrekidis, P. G., Frantzeskakis, D. J., Malomed, Boris A., Bishop, A. R.
We consider a system of two discrete nonlinear Schr\"{o}dinger equations, coupled by nonlinear and linear terms. For various physically relevant cases, we derive a modulational instability criterion...
Quantum correlations in bound-soliton pairs and trains in fiber lasers (2004)
Lee, Ray-Kuang, Lai, Yinchieh, Malomed, Boris A.
Quantum correlations in pairs and arrays (trains) of bound solitons modeled by the complex Ginzburg-Landau equation (CGLE) are calculated numerically, on the basis of linearized equations for quantum...
Stability and collisions of moving semi-gap solitons in Bragg cross-gratings (2004)
Mayteevarunyoo, T., Malomed, Boris A., Chu, P. L., Roeksabutr, A.
We report results of a systematic study of one-dimensional four-wave moving solitons in a recently proposed model of the Bragg cross-grating in planar optical waveguides with the Kerr nonlinearity;...
Slowdown and splitting of gap solitons in apodized Bragg gratings (2004)
Mak, William C. K., Malomed, Boris A., Chu, Pak L.
We study the motion of gap solitons in two models of apodized nonlinear fiber Bragg gratings (BGs), with the local reflectivity (LR) varying along the fiber. A single step of LR, and a periodic array...
Gubeskys, Arthur, Malomed, Boris A.
We consider continuous-wave (CW) states and dark solitons (DSs) in a system of two fundamental-frequency (FF) and one second-harmonic (SH) waves in a planar waveguide with the quadratic nonlinearity,...
Lee, Ray-Kuang, Lai, Yinchieh, Malomed, Boris A.
Small quantum fluctuations in solitons described by the cubic-quintic nonlinear Schr\"{o}dinger equation (CQNLSE) are studied with the linear approximation. The cases of both self-defocusing and...
Families of Matter-Waves for Two-Component Bose-Einstein Condensates (2003)
Kevrekidis, P. G., Nistazakis, H., Frantzeskakis, D. J., Malomed, Boris A., Carretero-González, R.
We produce several families of solutions for two-component nonlinear Schr\"{o}dinger/Gross-Pitaevskii equations. These include domain walls and the first example of an antidark or gray soliton in the...
Feng, Bao-Feng, Malomed, Boris A.
By means of the variational approximation (VA), a system of ordinary differential equations (ODEs) is derived to describe the propagation of antisymmetric solitons in a multi-channel (WDM) optical...
Solitons in a system of three linearly coupled fiber gratings (2003)
Gubeskys, Arthur, Malomed, Boris A.
We introduce a model of three parallel-coupled nonlinear waveguiding cores equipped with Bragg gratings (BGs), which form an equilateral triangle. The objective of the work is to investigate solitons...
Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation (2003)
Barashenkov, I. V., Cross, S., Malomed, Boris A.
It is well known that pulse-like solutions of the cubic complex Ginzburg-Landau equation are unstable but can be stabilised by the addition of quintic terms. In this paper we explore an alternative...
Moiseyev, Nimrod, Carr, L. D., Malomed, Boris A., Band, Y. B.
It is shown using the Gross-Pitaevskii equation that resonance states of Bose-Einstein condensates with attractive interactions can be stabilized into true bound states. A semiclassical variational...
Dark-in-Bright Solitons in Bose-Einstein Condensates with Attractive Interactions (2003)
Kevrekidis, P. G., Frantzeskakis, D. J., Malomed, Boris A., Bishop, A. R., Kevrekidis, I. G.
We demonstrate a possibility to generate localized states in effectively one-dimensional Bose-Einstein condensates with a negative scattering length in the form of a dark soliton in the presence of...
Formation of a Standing-Light Pulse through Collision of Gap Solitons (2003)
Mak, William C. K., Malomed, Boris A., Chu, Pak L.
Results of a systematic theoretical study of collisions between moving solitons in a fiber grating are presented. Various outcomes of the collision are identified, the most interesting one being...
Periodic waves in bimodal optical fibers (2003)
Chow, K. W., Nakkeeran, K., Malomed, Boris A.
We consider coupled nonlinear Schrodinger equations (CNLSE) which govern the propagation of nonlinear waves in bimodal optical fibers. The nonlinear transform of a dual-frequency signal is used to...
Domain Walls in Two-Component Dynamical Lattices (2003)
Kevrekidis, P. G., Malomed, Boris A., Frantzeskakis, D. J., Bishop, A. R.
We introduce domain-wall (DW) states in the bimodal discrete nonlinear Schr{\"{o}}dinger equation, in which the modes are coupled by cross phase modulation (XPM). By means of continuation from...
Interaction of a soliton with a local defect in a fiber Bragg grating (2002)
Mak, William C. K., Chu, Pak L., Malomed, Boris A.
We study the interactions of a Bragg-grating soliton with a localized attractive defect which is a combined perturbation of the grating and refractive index. A family of exact analytical solutions...
Interaction of a soliton with a localized gain in a fiber Bragg grating (2002)
Mak, William C. K., Chu, Pak L., Malomed, Boris A.
A model of a lossy nonlinear fiber grating with a "hot spot", which combines a local gain and an attractive perturbation of the refractive index, is introduced. A family of exact solutions for pinned...
Solitons in Bose-Einstein condensates trapped in a double-well potential (2002)
Shchesnovich, Valery S., Malomed, Boris A., Kraenkel, Roberto A.
We investigate, analytically and numerically, families of bright solitons in a system of two linearly coupled nonlinear Schrodinger/Gross-Pitaevskii equations, describing two Bose-Einstein...
Feng, Bao-Feng, Malomed, Boris A., Kawahara, Takuji
A two-dimensional (2D) generalization of the stabilized Kuramoto - Sivashinsky (KS) system is presented. It is based on the Kadomtsev-Petviashvili (KP) equation including dissipation of the generic...
Solitons in coupled Ablowitz-Ladik chains (2002)
Malomed, Boris A., Yang, Jianke
A model of two coupled Ablowitz-Ladik (AL) lattices is introduced. While the system as a whole is not integrable, it admits reduction to the integrable AL model for symmetric states. Stability and...
Stable periodic waves in coupled Kuramoto-Sivashinsky - Korteweg-de Vries equations (2002)
Feng, Bao-Feng, Malomed, Boris A., Kawahara, Takuji
Periodic waves are investigated in a system composed of a Kuramoto-Sivashinsky - Korteweg-de Vries (KS-KdV) equation, which is linearly coupled to an extra linear dissipative equation. The model...
Solitons in a Three-Wave System with Intrinsic Linear Mixing and Walkoff (2002)
Kaplan, Arkady, Malomed, Boris A.
A modification of the usual Type-II second-harmonic-generation model is proposed, which includes two additional features: linear conversion and walkoff (group-velocity difference) between two...
Sakaguchi, Hidetsugu, Malomed, Boris A.
Two models of driven optical cavities, based on two-dimensional Ginzburg-Landau equations, are introduced. The models include loss, the Kerr nonlinearity, diffraction in one transverse direction, and...
Embedded Solitons in Lagrangian and Semi-Lagrangian Systems (2002)
Kaup, D. J., Malomed, Boris A.
We develop the technique of the variational approximation for solitons in two directions. First, one may have a physical model which does not admit the usual Lagrangian representation, as some terms...
Scattering of a solitary pulse on a local defect or breather (2002)
Kevrekidis, Panayotis G., Malomed, Boris A., Nistazakis, H. E., Frantzeskakis, Dimitri J., Saxena, A., Bishop, A. R.
A model is introduced to describe guided propagation of a linear or nonlinear pulse which encounters a localized nonlinear defect, that may be either static or breather-like one (the model with the...
Spatial solitons in a medium composed of self-focusing and self-defocusing layers (2002)
Atai, Javid, Malomed, Boris A.
We introduce a model combining Kerr nonlinearity with a periodically changing sign ("nonlinearity management") and a Bragg grating (BG). The main result, obtained by means of systematic simulations,...
Noise-induced dephasing of an ac-driven Josephson junction (2002)
Filatrella, Giovanni, Malomed, Boris A., Pagano, Sergio
We consider phase-locked dynamics of a Josephson junction driven by finite-spectral-linewidth ac current. By means of a transformation, the effect of frequency fluctuations is reduced to an effective...
Progressive motion of an ac-driven kink in an annular damped system (2002)
Goldobin, Edward, Malomed, Boris A., Ustinov, Alexey V.
A novel dynamical effect is presented: systematic drift of a topological soliton in ac-driven weakly damped systems with periodic boundary conditions. The effect is demonstrated in detail for a long...
Cuspons, peakons and regular gap solitons between three dispersion curves (2002)
Grimshaw, Roger, Malomed, Boris A., Gottwald, Georg A.
A general wave model with the cubic nonlinearity is introduced to describe a situation when the linear dispersion relation has three branches, which would intersect in the absence of linear couplings...
Scheuer, Jacob, Malomed, Boris A.
We study, analytically and numerically, the dynamical behavior of the solutions of the complex Ginzburg-Landau equation with diffraction but without diffusion, which governs the spatial evolution of...
"Dispersion management" for solitons in a Korteweg-de Vries system (2001)
Clarke, Simon, Malomed, Boris A., Grimshaw, Roger
The existence of ``dispersion-managed solitons'', i.e., stable pulsating solitary-wave solutions to the nonlinear Schr\"{o}dinger equation with periodically modulated and sign-variable dispersion is...
Stationary states of Bose-Einstein condensates in single- and multi-well trapping potentials (2001)
D'Agosta, Roberto, Malomed, Boris A., Presilla, Carlo
The stationary solutions of the Gross-Pitaevskii equation can be divided in two classes: those which reduce, in the limit of vanishing nonlinearity, to the eigenfunctions of the associated...
Nonlinear parametric instability in double-well lattices (2001)
Riedel, Jaroslav, Majernikova, Eva, Malomed, Boris A.
A possibility of a nonlinear resonant instability of uniform oscillations in dynamical lattices with harmonic intersite coupling and onsite nonlinearity is predicted. Numerical simulations of a...
Families of Bragg-grating solitons in a cubic-quintic medium (2001)
Atai, Javid, Malomed, Boris A.
We investigate the existence and stability of solitons in an optical waveguide equipped with a Bragg grating (BG) in which nonlinearity contains both cubic and quintic terms. The model has...
Quadratic solitons in cubic crystals (2001)
Gisin, Boris V., Malomed, Boris A.
Starting from the Maxwell's equations and without resort to the paraxial approximation, we derive equations describing stationary (1+1)-dimensional beams propagating at an arbitrary direction in an...
One- and two-dimensional solitons in saturable media (2001)
Gisin, Boris V., Malomed, Boris A.
Very narrow spatial bright solitons in (1+1)D and (2+1)D versions of cubic-quintic and full saturable models are studied, starting from the full system of the Maxwell's equations, rather than from...
Dispersion management for solitons in a Korteweg-de Vries system (2001)
Clarke, Simon, Malomed, Boris A., Grimshaw, Roger H.J.
This is a pre-print. The definitive version: CLARKE, S., MALOMED, B.A. and GRIMSHAW, R., 2002. Dispersion management for solitons in a Korteweg-de Vries system. Chaos, 12(1), pp.8-15, is available...
Cuspons, peakons and regular gap solitons between three dispersion curves (2001)
Grimshaw, Roger H.J., Malomed, Boris A., Gottwald, Georg A.
This is a pre-print.
Cuspon and regular gap solitons between three dispersion curves (2001)
Grimshaw, Roger H.J., Malomed, Boris A.
This is a pre-print. The definitive version: GRIMSHAW, R. and MALOMED, B.A., 2002. Singular and regular gap solitons between three dispersion curves. Physical Review E, 65(6): Art. No. 066606 Part 2,...
Dispersion management for solitons in a Korteweg-de Vries system (2001)
Clarke, Simon R., Malomed, Boris A., Grimshaw, Roger H.J.
This is a pre-print. The definitive version: CLARKE, S., MALOMED, B.A. and GRIMSHAW, R., 2002. Dispersion management for solitons in a Korteweg-de Vries system. Chaos, 12(1), pp.8-15, is available...
Cuspons, peakons and regular gap solitons between three dispersion curves (2001)
Grimshaw, Roger H.J., Malomed, Boris A., Gottwald, Georg A.
This is a pre-print.
Propagation of an optical pulse in a fiber link with random dispersion management (2000)
Berntson, Anders, Malomed, Boris A.
A model of a long optical communication line consisting of alternating segments with anomalous and normal dispersion, whose lengths are picked up randomly from a certain interval, is considered. At...
Driben, Rodislav, Malomed, Boris A.
We consider a long fiber-optical link consisting of alternating dispersive and nonlinear segments, i.e., a split-step model (SSM), in which the dispersion and nonlinearity are completely separated....
Bragg-grating solitons in a semilinear dual-core system (2000)
Atai, Javid, Malomed, Boris A.
We investigate the existence and stability of gap solitons in a double-core optical fiber, where one core has the Kerr nonlinearity and the other one is linear, with the Bragg grating (BG) written on...
Breathing and randomly walking pulses in a semilinear Ginzburg-Landau system (2000)
Sakaguchi, Hidetsugu, Malomed, Boris A.
A system consisting of the cubic complex Ginzburg-Landau equation which is linearly coupled to an additional linear dissipative equation, is considered. The model was introduced earlier in the...
A Quasicrystallic Domain Wall in Nonlinear Dissipative Patterns (2000)
Malomed, Boris A., Rotstein, Horacio G.
We propose an indirect approach to the generation of a two-dimensional quasiperiodic (QP) pattern in convection and similar nonlinear dissipative systems where a direct generation of stable uniform...
Clarke, S. R., Grimshaw, R. H. J., Malomed, Boris A.
We consider in detail the self-trapping of a soliton from a wave pulse that passes from a defocussing region into a focussing one in a spatially inhomogeneous nonlinear waveguide, described by a...
Kink in a periodically modulated disordered system (1999)
Majernikova, Eva, Riedel, Jaroslav, Malomed, Boris A.
We consider a dc-driven damped sine-Gordon model with a small nonlinear spatial-disorder term, onto which a sinusoidal modulation is superimposed. It describes, e.g., a weakly disordered system with...
Moving Embedded Solitons (1999)
Champneys, Alan R, Malomed, Boris A
The first theoretical results are reported predicting {\em moving} solitons residing inside ({\it embedded} into) the continuous spectrum of radiation modes. The model taken is a Bragg-grating medium...
Embedded Solitons in a Three-Wave System (1999)
Champneys, Alan R., Malomed, Boris A.
We report a rich spectrum of isolated solitons residing inside ({\it embedded } into) the continuous radiation spectrum in a simple model of three-wave spatial interaction in a...
"Quadratic solitons" in nonlinear dynamiical latticess (1999)
Konotop, Vladimir V., Malomed, Boris A.
We propose a lattice model, in both one- and multidimensional versions, which may give rise to matching conditions necessary for the generation of solitons through the second-harmonic generation. The...
The ac-Driven Motion of Dislocations in a Weakly Damped Frenkel-Kontorova Lattice (1999)
Filatrella, Giovanni, Malomed, Boris A.
By means of numerical simulations, we demonstrate that ac field can support stably moving collective nonlinear excitations in the form of dislocations (topological solitons, or kinks) in the...
Crystallization Kinetics in the Swift--Hohenberg Model (1999)
Aranson, Igor S., Malomed, Boris A., Pismen, Len M., Tsimring, Lev S.
It is shown numerically and analytically that the front propagation process in the framework of the Swift-Hohenberg model is determined by periodic nucleation events triggered by the explosive growth...
Standing and Moving Gap Solitons in Resonantly Absorbing Gratings (1998)
Kozhekin, A. E., Kurizki, G., Malomed, Boris A.
We present hitherto unknown forms of soliton dynamics in the forbidden frequency gap of a Bragg reflector, modified by periodic layers of near-resonant two-level systems (TLS). Remarkably, even...
A Potential of Interaction between Two- and Three-Dimensional Solitons (1998)
A general method to find an effective potential of interaction between far separated 2D and 3D solitons is elaborated, including the case of 2D vortex solitons. The method is based on explicit...
Stationary states of the Gross-Pitaevskii equation with linear counterpart (1998)
D'Agosta, Roberto, Malomed, Boris A., Presilla, Carlo
We study the stationary solutions of the Gross-Pitaevskii equation that reduce, in the limit of vanishing non-linearity, to the eigenfunctions of the associated Schr\"odinger equation. By providing...
Soliton motion in a parametrically ac-driven damped Toda lattice (1998)
Rasmussen, K. O., Malomed, Boris A., Bishop, A. R., Gronbech-Jensen, Niels
We demonstrate that a staggered parametric ac driving term can support stable progressive motion of a soliton in a Toda lattice with friction, while an unstaggered drivng force cannot. A physical...
Thirring Solitons in the presence of dispersion (1998)
Champneys, Alan R, Malomed, Boris A, Friedman, Mark J
The effect of dispersion or diffraction on zero-velocity solitons is studied for the generalized massive Thirring model describing a nonlinear optical fiber with grating or parallel-coupled planar...
Inverse ac Josephson Effect for a Fluxon in a Long Modulated Junction (1994)
Filatrella, Giovanni, Malomed, Boris A., Parmentier, Robert D.
We analyze motion of a fluxon in a weakly damped ac-driven long Josephson junction with a periodically modulated maximum Josephson current density. We demonstrate both analytically and numerically...
Institute for Electromagnetic Field Theory and Plasma Physics, (1994)
Pak L. Chu, Yuri S. Kivshar, Boris A. Malomed, Gang-ding Peng
We propose an exactly solvable model of soliton-based pulse control that describes the physically important situation when the soliton period is much longer than the length of the coupling region in...
Interactions Between Solitons in a Monomode Fiber, (1992)
In the present work, pairwise interactions between solitons are considered in two models of a nonlinear monomode fiber. The first model is the simplest one to describe the competition between losses...
SOLITONS IN A SYSTEM OF COUPLED KORTEWEG-DE VRIES EQUATIONS (1988)
Yuri S. Kivshar, Boris A. Malomed
A system of two Korteweg-de Vries equations coupled by small linear and nonlinear terms, which is a model of a resonant interaction between two internal gravity-wave modes in a shallow stratified...
RADIATIVE AND INELASTIC EFFECTS IN DYNAMICS OF DOUBLE SINE-GORDON SOLITONS (1987)
Yuri S. Kivshar, Boris A. Malomed
The dynamics ofthe so-called wobblers, i.e. 4it-kinks ofthe double sine-Gordon equation with excited internal oscillations, is studied. The rate of energy emission from a weakly excited wobbler is...
Yuri S. Kivshar, Boris A. Malomed
Radiative effects accompanying a fluxon—antifluxon collision on the background of a localized inhomogeneity (microshortor microresistance) or in a randomly inhomogeneous long Josephson junction...
North-Holland, Amsterdam MANY-PARTICLE EFFECTS IN NEARLY INTEGRABLE SYSTEMS (1985)
Yuri S. Kivshar, Boris A. Malomed
For the sine-Gordon and nonlinear Schr~Sdinger equations with conservative perturbations three-particle effects in collision of a fast soliton with two more slow ones are considered in the first...