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 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 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 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...

For two-dimensional condensates, we introduce patterns formed by intersection of domain-walls (DWs) between immiscible species. Both symmetric and asymmetric cases are investigated, with equal or different numbers N1,2 of atoms in the two species. The case of a rotating trap is considered too....

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 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 propose a versatile variational method to investigate the spatio-temporal dynamics of one-dimensional magnetically-trapped Bose-condensed gases. To this end we employ a q-Gaussian trial wave-function that describes both the low- and the high-density limit of the ground state of a...

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...