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We generalize recent work on parametric resonances for nonlinear Schrödinger (NLS) type equations to the case of three dimensional BoseEinstein condensates at zero temperatures. We show the poss...
We introduce the concept of ring dark solitons in Bose-Einstein condensates. We show that relatively shallow rings are not subject to the snake instability, but a deeper ring splits into a robust ring...
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 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 an...
We investigate the modulational instability of nonlinear Schrödinger equations with periodic variation of their coefficients. In particular, we focus on the case of the recently proposed, experim...
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 BoseEinstein con...
For a Bose-Einstein condensate (BEC) in a two-dimensional (2D) trap, we introduce cross patterns, which are generated by the intersection of two domain walls (DWs) separating immiscible species, with ...
This paper is concerned with the long-wavelength instabilities (infrared catastrophes) occurring in Bose-Einstein condensates (BECs). We examine the modulational instability in “cigar-shaped” (one-dim...
In this short topical review, we revisit a number of works on the pattern-forming dynamical instabilities of BoseEinstein condensates in one- and two-dimensional settings. In particular, we illustrat...
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 Fermi–Pasta–Ulam (FPU) model, which was proposed 50 years ago to examine thermalization in nonmetallic solids and develop “experimental” techniques for studying nonlinear problems, continues...
We consider the Gross--Pitaevskii (GP) equation in the presence of periodic and quasi-periodic superlattices to study cigar-shaped Bose--Einstein condensates (BECs) in such potentials. We examine spat...
We consider a one-dimensional defocusing Gross–Pitaevskii equation with a parabolic potential. Dark solitons oscillate near the center of the potential trap and their amplitude decays due to radiative...
A theory of the nonsymmetric Landau-Zener tunneling of Bose-Einstein condensates in deep optical lattices is presented. It is shown that periodic exchange of matter between the bands is described by a...
We demonstrate the possibility of creating domain walls described by a single component Gross–Pitaevskii equation with attractive interactions, in the presence of an optical–lattice potential. While i...

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