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We study the existence and stability of localized states in the discrete nonlinear Schrödinger equation on two-dimensional nonsquare lattices. The model includes both the nearest-neighbor and lon...
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 develop an averaging method for solitons of the nonlinear Schrödinger equation with a periodically varying nonlinearity coefficient, which is used to effectively describe solitons in Bose-Eins...
We investigate the stability of dark solitons (DSs) in an effectively one-dimensional Bose-Einstein condensate in the presence of the magnetic parabolic trap and an optical lattice (OL). The analysis ...
A model including two nonlinear chains with linear and nonlinear couplings between them, and opposite signs of the discrete diffraction inside the chains, is introduced. In the case of the cubic [ χ(3...
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...
The dynamics of linear and nonlinear excitations in a Bose gas in the Tonks-Girardeau regime with longitudinal confinement are studied within a mean-field theory of quintic nonlinearity. A reductive p...
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...
We consider the discrete solitons bifurcating from the anti-continuum limit of the discrete nonlinear Schrödinger (NLS) lattice. The discrete soliton in the anti-continuum limit represents an arb...
Motivated by the recent experimental achievements in the work with Bose-Einstein condensates (BECs), we consider bright matter-wave solitons, in the presence of a parabolic magnetic trap and a spatial...
We consider the effects of anisotropy on solitons of various types in two-dimensional nonlinear lattices, using the discrete nonlinear Schrödinger equation as a paradigm model. For fundamental so...
We examine the dynamics of a bright solitary wave in the presence of a repulsive or attractive localized “impurity” in Bose–Einstein condensates (BECs). We study the generation and stability of a pair...
We demonstrate that time-periodic modulation of the nonlinearity coefficient in the discrete nonlinear Schrödinger equation strongly facilitates creation of traveling solitons in the lattice. We ...
We investigate bright matter-wave solitons in the presence of a spatially varying scattering length. It is demonstrated that a soliton can be confined due to the inhomogeneous collisional interactions...
We study the existence and stability of bright, dark, and gap matter-wave solitons in optical superlattices. Then, using these properties, we show that (time-dependent) “dynamical superlattices” can b...

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