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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...
Radially symmetric nonlinear states of harmonically trapped Bose-Einstein condensates
Spectrum quantum harmonic oscillator nonlinear function linear stability
2014/12/25
Starting from the spectrum of the radially symmetric quantum harmonic oscillator in two dimensions, we create a large set of nonlinear solutions. The relevant three principal branches, with nr=0,1, an...
Nonlinear waves in Bose-Einstein condensates: physical relevance and mathematical techniques
Physical concept nonlinear wave condensate the atoms
2014/12/24
The aim of this review is to introduce the reader to some of the physical notions and the mathematical methods that are relevant to the study of nonlinear waves in Bose–Einstein condensates (BECs). Up...
Generalized neighbor-interaction models induced by nonlinear lattices
Nonlinear schrodinger equation the space nonlinear coefficient complex nonlinear lattice
2014/12/24
It is shown that the tight-binding approximation of the nonlinear Schrödinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of no...
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...
Soliton dynamics in linearly coupled discrete nonlinear Schrodinger equations
Soliton dynamics system coupling discrete nonlinear schrodinger equation
2014/12/24
We study soliton dynamics in a system of two linearly coupled discrete nonlinear Schrödinger equations, which describe the dynamics of a two-component Bose gas, coupled by an electromagnetic fiel...
Highly nonlinear solitary waves in heterogeneous periodic granular media
Numerical simulation of highly nonlinear solitary wave dimer and trimer one-dimensional particle lattice structure
2014/12/24
We use experiments, numerical simulations, and theoretical analysis to investigate the propagation of highly nonlinear solitary waves in periodic arrangements of dimer (two-mass) and trimer (three-mas...
Non-nearest-neighbor interactions in nonlinear dynamical lattices
Discrete nonlinear schrodinger equation the nonlinear dynamic systematic zero coupling
2014/12/24
We revisit the theme of non-nearest-neighbor interactions in nonlinear dynamical lattices, in the prototypical setting of the discrete nonlinear Schrödinger equation. Our approach offers a system...
Nucleation of Breathers via Stochastic Resonance in Nonlinear Lattices
Staggered driving force the nonlinear discrete model discrete respirator resonance phenomenon
2014/12/24
By applying a staggered driving force in a prototypical discrete model with a quartic nonlinearity, we demonstrate the spontaneous formation and destruction of discrete breathers with a selected frequ...
Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrodinger lattices
Stability liquidity discrete soliton three-dimensional nonlinear
2014/12/24
We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schrödinger lattices with a combination of cubic self-focusing and quintic...
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...
Effects of Long-Range Nonlinear Interactions in Double-Well Potentials
The structure nonlinear nonlinear optics matter waves
2014/12/24
We consider the interplay of linear double-well-potential (DWP) structures and nonlinear longrange interactions of different types, motivated by applications to nonlinear optics and matter waves. We f...
Short pulse equations and localized structures in frequency band gaps of nonlinear metamaterials
Short pulse propagation nonlinear metamaterials nonlinear dielectric short pulse linear electromagnetic waves magnetic permeability
2014/12/24
We consider short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. Two short-pulse equations (SPEs) are derived for the high- a...
Nonlinear waves in disordered diatomic granular chains
Nonlinear wave propagation and scattering disordered particle chain ball statistical mechanics particle chains
2014/12/24
We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas f...