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A Liapunov Bound for Solutions of Poisson’s Equation
Markov chain Markov process Poisson equation Liapounov function
2015/7/8
In this paper we consider ψ-irreducible Markov processes evolving in discrete or continuous time on a general state space. We develop a Liapounov function criterion that permits one to obtain explicit...
Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential
Walter's function nonlinear schrodinger equation periodic vector lattice
2014/12/29
In the present paper we use the Wannier function basis to construct lattice approximations of the nonlinear Schrödinger equation with a periodic potential. We show that the nonlinear Schrödi...
Breather lattice and its stabilization for the modified Korteweg–de Vries equation
Breathing lattice vries equation the numerical simulation of breathing lattice
2014/12/29
We obtain an exact solution for the breather lattice solution of the modified Korteweg–de Vries equation. Numerical simulation of the breather lattice demonstrates its instability due to the breather-...
Parametric and modulational instabilities of the discrete nonlinear Schrödinger equation
The coupling instability discrete nonlinear schrodinger equation condensate dynamics
2014/12/29
We examine the parametric and modulational instabilities arising in a non-autonomous, discrete nonlinear Schrödinger equation. The principal motivation for our study stems from the dynamics of Bo...
On the Modulational Instability of the Nonlinear Schrödinger Equation with Dissipation
Space is unified nonlinear schrodinger equation the high order dissipation condensate
2014/12/29
The modulational instability (MI) of spatially uniform states in the nonlinear Schrödinger (NLS) equation is examined in the presence of higher-order dissipation. The study is motivated by result...
Low regularity solutions to a gently stochastic nonlinear wave equation in nonequilibrium statistical mechanics
System stochastic partial differential equations the nonlinear medium heat transfer and energy
2014/12/29
We consider a system of stochastic partial differential equations modeling heat conduction in a non-linear medium. We show global existence of solutions for the system in Sobolev spaces of low regular...
Equation-free dynamic renormalization in a glassy compaction model
In combination with dynamic renormalization evolutionary dynamics accelerated simulator glass dynamic phenomenon
2014/12/25
Combining dynamic renormalization with equation-free computational tools, we study the apparently asymptotically self-similar evolution of void distribution dynamics in the diffusion-deposition proble...
From Feshbach-resonance managed Bose-Einstein condensates to anisotropic universes: Applications of the Ermakov-Pinney equation with time-dependent nonlinearity
Two-dimensional condensate time-varying magnetic confinement scattering wave function ordinary differential equations
2014/12/25
In this work we revisit the topic of two-dimensional Bose–Einstein condensates under the influence of time-dependent magnetic confinement and time-dependent scattering length. A moment approach reduce...
Asymptotic stability of small solitons in the discrete nonlinear Schr¨odinger equation in one dimension
Small solitary wave one dimensional discrete nonlinear septic nonlinear power law equation
2014/12/25
Asymptotic stability of small solitons in one dimension is proved in the framework of a discrete nonlinear Schr¨odinger equation with septic and higher power-law nonlinearities and an external potenti...
Approximation of Solitons in the Discrete NLS Equation
Discrete soliton one dimensional discrete nonlinear schrodinger equation
2014/12/24
We study four different approximations for finding the profile of discrete solitons in the one- dimensional Discrete Nonlinear Schrödinger (DNLS) Equation. Three of them are discrete approximatio...
Two-dimensional paradigm for symmetry breaking: The nonlinear Schroumldinger equation with a four-well potential
Mechanical systems linear geometric properties nonlinear dynamic equations
2014/12/24
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derive...
Vortex solutions of the discrete Gross-Pitaevskii equation starting from the anti-continuum limit
Dark vortex dynamic evolution two-dimensional discrete nonlinear schrodinger defocused model
2014/12/24
In this paper, we consider the existence, stability and dynamical evolution of dark vortex states in the two-dimensional defocusing discrete nonlinear Schrödinger model, a model of interest both ...
Azimuthal modulational instability of vortices in the nonlinear Schrodinger equation
Vortex the two-dimensional nonlinear Lagrange function one-dimensional azimuth equation of motion the Fourier model of spatial orientation
2014/12/24
We study the azimuthal modulational instability of vortices with different topological charges, in the focusing two-dimensional nonlinear Schrödinger (NLS) equation. The method of studying the st...
Existence, Stability, and Dynamics of Bright Vortices in the Cubic-Quintic Nonlinear Schr¨odinger Equation
Eddy current stable coupling two-dimensional whirlpool coupling whirlpool
2014/12/24
We study the existence and azimuthal modulational stability of vortices in the two-dimensional (2D) cubic-quintic nonlinear Schr¨odinger (CQNLS) equation. We use a variational approximation (VA) based...
On Approximation of the Backward Stochastic Differential Equation
Backward SDE approximation of the solution small noise asymptotics
2013/6/14
We consider the problem of approximation of the solution of the backward stochastic differential equation in the Markovian case. We suppose that the trend coefficient of the diffusion process depends ...