A Dihedral Acute Triangulation of the Cube (2009)
VanderZee, Evan, Hirani, Anil N., Zharnitsky, Vadim, Guoy, Damrong
It is shown that there exists a dihedral acute triangulation of the three-dimensional cube. The method of constructing the acute triangulation is described, and symmetries of the triangulation are...
(1) QUASI-LINEAR DYNAMICS IN NONLINEAR SCHRÖDINGER EQUATION WITH PERIODIC BOUNDARY CONDITIONS (2009)
M. Burak, Erdo Gan, Vadim Zharnitsky
Abstract. It is shown that a large subset of initial data with finite energy (L 2 norm) evolves nearly linearly in nonlinear Schrödinger equation with periodic boundary conditions. These new...
Averaging of dispersion-managed solitons: Existence and stability (2009)
Dmitry E. Pelinovsky, Vadim Zharnitsky
Abstract. We consider existence and stability of dispersion-managed solitons in the two approximations of the periodic nonlinear Schrödinger (NLS) equation: (i) a dynamicalsystem for a Gaussian...
Periodic Orbits in Outer Billiard (2008)
It is shown that the set of 4-period orbits in outer billiard in the Euclidean plane with piecewise smooth convex boundary has an empty interior, provided that no four corners of the boundary form a...
Sub-Riemannian geometry and periodic orbits in classical billiards (2008)
Yuliy Baryshnikov, Vadim Zharnitsky
Abstract. Classical (Birkhoff) billiards with full 1-parameter families of periodic orbits are considered. It is shown that construction of a convex billiard with a “rational” caustic (i.e....
A REACTION DISPERSION SYSTEM AND RAMAN INTERACTIONS ∗ (2008)
Michael I. Weinstein, Vadim Zharnitsky
Abstract. We consider the problem of amplification of an optical signal wave with an optical pump wave when both are propagating in the fundamental mode of a single mode optical waveguide. We...
Quasi-linear dynamics in nonlinear Schr\" odinger equation with periodic boundary conditions (2007)
Erdogan, M. Burak, Zharnitsky, Vadim
It is shown that a large subset of initial data with finite energy ($L^2$ norm)evolves nearly linearly in nonlinear Schr\" odinger equation with periodic boundary conditions. These new solutions are...
Periodic orbits in outer billiards (2006)
Tumanov, Alexander, Zharnitsky, Vadim
It is shown that the set of 4-period orbits in outer billiard with piecewise smooth convex boundary has an empty interior, provided that no four corners of the boundary form a parallelogram.
On sharp Strichartz inequalities for low dimensions (2006)
Dirk Hundertmark, Vadim Zharnitsky
The solution u to the free Schrödinger equation i∂tu =−Δu on R d
On sharp Strichartz inequalities for low dimensions (2006)
Dirk Hundertmark, Vadim Zharnitsky
Abstract. Recently Foschi gave a proof of a sharp Strichartz inequality in one and two dimensions. In this note, a new representation in terms of an orthogonal projection operator is obtained for the...
On sharp Strichartz inequalities for low dimensions (2006)
Dirk Hundertmark, Vadim Zharnitsky
Abstract. Recently Foschi gave a proof of a sharp Strichartz inequality in one and two dimensions. In this note, a new representation in terms of an orthogonal projection operator is obtained for the...
On sharp Strichartz inequalities in low dimensions (2006)
Hundertmark, Dirk, Zharnitsky, Vadim
Recently, Foschi gave a proof of a sharp Strichartz inequality in one and two dimensions. In this paper, a new representation in terms of an orthogonal projection operator is obtained for the...
Periodic orbits in outer billiard (2006)
Tumanov, Alexander, Zharnitsky, Vadim
It is shown that the set of 4-period orbits in outer billiard in the Euclidean plane with piecewise smooth convex boundary has an empty interior, provided that no four corners of the boundary form a...
Abstract: It is shown that a large class of solutions in two-degree-of-freedom Hamiltonian systems of billiard type can be described by slowly varying one-degree-of-freedom Hamiltonian systems. Under...
Parametrically forced sine-Gordon equation and domain walls dynamics in ferromagnets (1998)
Zharnitsky, Vadim, Mitkov, Igor, Levi, Mark
A parametrically forced sine-Gordon equation with a fast periodic {\em mean-zero} forcing is considered. It is shown that $\pi$-kinks represent a class of solitary-wave solutions of the equation....
$\pi$-kinks in strongly ac driven sine-Gordon systems (1998)
Zharnitsky, Vadim, Mitkov, Igor, Grønbech-Jensen, Niels
We demonstrate that $\pi$-kinks exist in non-parametrically ac driven sine-Gordon systems if the ac drive is sufficiently fast. It is found that, at a critical value of the drive amplitude, there are...
Higher order Shapiro steps in ac-driven Josephson junctions (1998)
Rasmussen, Kim O., Zharnitsky, Vadim, Mitkov, Igor, Grønbech-Jensen, Niels
We demonstrate that the well known phase-locking mechanism leading to Shapiro steps in ac-driven Josephson junctions is always accompanied by a higher order phase-locking mechanism similar to that of...
Institute for Mathematical Research
pi-kinks in Strongly AC Driven Sine-Gordon Systems (1998)
Vadim Zharnitsky, Igor Mitkov, Niels Grønbech-Jensen, Niels Gr��nbech-jensen
We demonstrate that ß-kinks can exist in non-parametrically AC driven sineGordon systems if the AC drive is sufficiently fast. It is found that, at a critical value of the drive amplitude, there are...
Abstract: Based on the KAM theory, investigation of the equation of motion of a classical particle in a one-dimensional superquadratic potential well, under the influence of an external time-periodic...