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 it is found that the domain wall is unstable in an infinite system, we show that the external...

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 field, and confined in a strong optical lattice. When the nonlinear coupling strengths are equal, we use...

We explore spatially extended dynamical states in the discrete nonlinear Schrödinger lattice in two- and three-dimensions, starting from the anti-continuum limit. We first consider the “core” of the relevant states (either a two-dimensional “tile” or a three-dimensional “stone”),...

We numerically study the nucleation of gray solitons and vortex–antivortex pairs created by a moving impurity in, respectively, 1D and 2D Bose–Einstein condensates (BECs) confined by a parabolic potential. The simulations emulate the motion of a localized laser-beam spot through the trapped...

We study the dynamics of dark solitons in spatially inhomogeneous media with applications to cigar-shaped Bose–Einstein condensates trapped in a harmonic magnetic potential and a periodic potential representing an optical lattice. We distinguish and systematically investigate the cases with...

We study the dynamics of atomic Bose–Einstein condensates (BECs), when the quadrupole mode is excited. Within the Thomas–Fermi approximation, we derive an exact first-order system of differential equations that describes the parameters of the BEC wave function. Using perturbation theory...

We revisit the topic of the existence and azimuthal modulational stability of solitary vortices (alias vortex solitons) in the two-dimensional (2D) cubic–quintic nonlinear Schrödinger equation. We develop a semi-analytical approach, assuming that the vortex soliton is relatively narrow, which...

We study the dynamics of solitons in Bose–Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. Chiefly, the one-dimensional (1D) case is considered. First, we demonstrate analytically that, in the case of the repulsive BEC,...

We describe a novel class of solitary waves in second-harmonic-generation models with competing quadratic and cubic nonlinearities. These solitary waves exist at a discrete set of values of the propagation constants, being embedded inside the continuous spectrum of the linear system (“embedded...

In this short communication we study compactons in the setting of discrete nonlinear Klein–Gordon (DNKG) chains. The temporal and spatial dependences of the solutions are separated resulting in an array of coupled nonlinear algebraic equations for the spatial dependence and an ordinary...