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We present a comprehensive analysis of the form and interaction of dipolar bright solitons across the full parameter space afforded by dipolar Bose-Einstein condensates, revealing the rich behaviour introduced by the non-local nonlinearity.…
We analyse the rotation of bright solitary waves formed of atomic Bose-Einstein condensates with attractive atomic interactions. By employing a variational technique and assuming an irrotational quadrupolar flow field, we map out the…
Employing a particularly suitable higher order symplectic integration algorithm, we integrate the 1-$d$ nonlinear Schr\"odinger equation numerically for solitons moving in external potentials. In particular, we study the scattering off an…
Inspired by experiments on Bose-Einstein condensates in optical lattices, we study the quantum evolution of dark soliton initial conditions in the context of the Bose-Hubbard Hamiltonian. An extensive set of quantum measures is utilized in…
We propose a scheme for the creation of stable three dimensional bright solitons in Bose-Einstein condensates, i.e., the matter-wave analog of so-called spatio-temporal "light bullets". Off-resonant dressing to Rydberg $nD$-states is shown…
In recent years, bright soliton-like structures composed of gaseous Bose-Einstein condensates have been generated at ultracold temperature. The experimental capacity to precisely engineer the nonlinearity and potential landscape experienced…
We study formation of solitons induced by counterflows of immiscible superfluids. Our setting is based on a quasi-one-dimensional binary Bose-Einstein condensate (BEC), composed of two immiscible components with large and small numbers of…
We consider the collision of a dark soliton with an obstacle in a quasi-one-dimensional Bose condensate. We show that in many respects the soliton behaves as an effective classical particle of mass twice the mass of a bare particle,…
We discuss the dynamics of interacting atomic bright solitons and dark bubbles in bulk immiscible Bose-Einstein condensates. Coherent matter-wave clusters can be constructed using dark-bright pairs with appropriate phases. In two dimensions…
Bright and dark solitons of the cubic nonlinear Schrodinger equation are used to construct complex-valued potentials with all-real spectrum. The real part of these potentials is equal to the intensity of a bright soliton while their…
It has been established for some time that high-power pump can trap a probe beam of lower intensity that is simultaneously propagating in a Kerr-type optical medium, inducing a focusing of the probe with the emergence of modes displaying…
We investigate, analytically and numerically, families of bright solitons in a system of two linearly coupled nonlinear Schrodinger/Gross-Pitaevskii equations, describing two Bose-Einstein condensates trapped in an asymmetric double-well…
We demonstrate that incoherent photon scattering by a Bose-Einstein condensate of non-ideal atomic gas is enhanced due to bosonic stimulation of spontaneous emission, similarly to coherent scattering in forward direction. Necessary initial…
The interaction of nonlinear Schr\"{o}dinger (NLS) solitons with potential wells with variable shapes is investigated numerically. For fixed initial velocities below the threshold for transmission, the outcome pattern as a function of the…
Starting with a Gaussian variational ansatz, we predict anisotropic bright solitons in quasi-2D Bose-Einstein condensates consisting of atoms with dipole moments polarized \emph{perpendicular} to the confinement direction. Unlike isotropic…
We demonstrate the existence of a new class of two-component vector solitary waves in which dispersion coefficients have of opposite signs. Stability is achieved by inclusion of an additional linear coupling between the vector components…
We investigate numerically and theoretically the conditions leading to soliton ejection stimulated through the scattering of bright solitons by modulated reflectionless potential wells. Such potential wells allow for the possibility of…
Adopting a mean-field description for a two-component atomic Bose-Einstein condensate, we study the stat- ics and dynamics of dark-bright solitons in the presence of localized impurities. We use adiabatic perturbation theory to derive an…
We study fast-moving bright solitons in the focusing nonlinear Schr\"odinger equation perturbed by a narrow Gaussian potential barrier. In particular, we present a general and comprehensive analysis of the case where two fast-moving bright…
This paper reviews theoretical advances on the formation and stabilization of multidimensional solitons in nonlinear Schr\"odinger systems with attractive interactions, focusing on atomic Bose-Einstein condensates and nonlinear optics.…