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This article studies the parabolic system of equations which is closely related to multitype branching Brownian motion. Particular attention is paid to the monotone traveling wave solutions of this sy...
This article studies the parabolic system of equations which is closely related to multitype branching Brownian motion. Particular attention is paid to the monotone traveling wave solutions of this sy...
We produce several families of solutions for two-component nonlinear Schrödinger/Gross-Pitaevskii equations. These include domain walls and the first example of an antidark or gray soliton in one...
We consider a system of two Gross–Pitaevskii (GP) equations, in the presence of an optical-lattice (OL) potential, coupled by both nonlinear and linear terms. This system describes a Bose–Einstein con...
In a benchmark dynamical-lattice model in three dimensions, the discrete nonlinear Schrödinger equation, we find discrete vortex solitons with various values of the topological charge S. Stabilit...
In this paper, an exact unitary transformation is examined that allows for the construction of solutions of coupled nonlinear Schrödinger equations with additional linear field coupling, from sol...
The long-standing problem of moving discrete solitary waves in nonlinear Schrödinger lattices is revisited. The context is photorefractive crystal lattices with saturable nonlinearity whose grand...
In this paper, we examine in detail the principal branches of solutions that arise in vector discrete models with nonlinear intercomponent coupling and four wave mixing. The relevant four branches of ...
In this work, we systematically generalize the Evans function methodology to address vector systems of discrete equations. We physically motivate and mathematically use as our case example a vector fo...
In this paper, we study the competition of the linear and nonlinear lattices and its effects on the stability and dynamics of bright solitary waves. We consider both lattices in a perturbative framewo...
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 “collisionally i...
Motivated by recent experiments on Faraday waves in Bose-Einstein condensates we investigate both analytically and numerically the dynamics of cigar-shaped Bose-condensed gases subject to periodic mod...
We propose a new type of waveforms in two-dimensional (2D) and three-dimensional (3D) discrete media-multilegged extended nonlinear structures (ENSs), built as arrays of lattice solitons (tiles and st...
We investigate the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic arra...
We consider the problem of the existence of a dynamical barrier of “mass” that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlin...

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