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A very natural construction of integrable extensions of soliton systems is presented. The extension is made on the level of evolution equations by a modification of the algebra of dynamical fields. The paper is motivated by recent works of…
An interplay of optical lattices and nonlinear impurities in controlling the dynamics of Bose-Einstein condensate bright solitons is investigated using effective potential approach. The ability of pushing the solitons into or away from the…
We consider one-dimensional solitons in a binary Bose-Einstein condensate with linear coupling between the components, trapped in an optical-lattice potential. The inter-species and intra-species interactions may be both repulsive or…
Manipulating nonlinear excitations, including solitons and vortices, is an essential topic in quantum many-body physics. A recent progress in this direction is a new protocol proposed in [Phys. Rev. Res. 2, 043256 (2020)] to produce dark…
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with low-dimensional (1D) conservative plus dissipative nonlinear optical lattices are investigated. In the case of focusing media (with attractive…
We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates (BECs). Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our…
Mixed type (bright-dark) soliton solutions of the integrable N-coupled nonlinear Schr{\"o}dinger (CNLS) equations with mixed signs of focusing and defocusing type nonlinearity coefficients are obtained by using Hirota's bilinearization…
We study the formation and dynamics of bright solitons in a quasi-one-dimensional reduced mean-field Gross-Pitaevskii equation of a dipolar Bose-Einstein condensate with repulsive short-range interactions. The study is carried out using a…
We investigate the dynamics of two miscible superfluids experiencing fast counterflow in a narrow channel. The superfluids are formed by two distinguishable components of a trapped dilute-gas Bose-Einstein condensate (BEC). The onset of…
We examine the effect of dissipation on traveling waves in nonlinear dispersive systems modeled by Benjamin- Bona- Mahony (BBM)-like equations. In the absence of dissipation the BBM-like equations are found to support soliton and…
The evolution of vector solitons under nonlinearity management is studied. The averaged over strong and rapid modulations in time of the inter-species interactions vector Gross-Pitaevskii equation (GPE) is derived. The averaging gives the…
We analyze the dynamics of two-component vector solitons, namely bright-in-dark solitons, via the variational approximation in Bose-Einstein condensates. The system is described by a vector nonlinear Schr\"odinger equation appropriate to…
We propose and analyze a scheme to create dark solitons and vortices in Bose-Einstein condensates. This is achieved starting from a condensate in the internal state $|a>$ and transferring the atoms to the internal state $|b>$ via a Raman…
We present families of beating dark-dark solitons in spin-orbit (SO) coupled Bose-Einstein condensates. These families consist of solitons residing simultaneously in the two bands of the energy spectrum. The soliton components are…
We demonstrate that the fission of higher-order N-solitons with a subsequent ejection of fundamental quasi-solitons creates solitonic cavities, formed by a pair of solitons with dispersive light trapped between them. As a result of multiple…
We simulate and analyze an experimental method of loading interacting ultracold atoms onto nontrivial quantum states such as nonlinear Bloch wave and soliton solutions in a 1-dimensional bichromatic lattice. Of standard bands, inverted…
In this paper, we study the dynamics of an interesting class of vector solitons in the long wave-short wave resonance interaction (LSRI) system. The model that we consider here describes the nonlinear interaction of the long-wave and…
We demonstrate fast control of the interatomic interactions in a Bose-Einstein condensate by coherently coupling two atomic states with intra- and inter-state scattering lengths of opposite signs. We measure the elastic and inelastic…
We report on the formation of dark discrete solitons in a nonlinear periodic system consisting of evanescently-coupled channel waveguides that are fabricated in defocusing lithium niobate. Localized nonlinear dark modes displaying a phase…
Motivated by recent proposals of ``collisionally inhomogeneous'' Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we study the existence and stability properties of bright and dark matter-wave solitons…