Related papers: Solitons in inhomogeneous gauge potentials: integr…
We report on the existence and stability of freely moving solitons in a spatially inhomogeneous Bose- Einstein condensate with helicoidal spin-orbit (SO) coupling. In spite of the periodically varying parameters, the system allows for the…
We consider a model of the exciton-polariton condensate based on a system of two Gross-Pitaevskii equations coupled by the second-order differential operator, which represents the spin-orbit coupling (SOC) in the system. Also included are…
We review spectral theory of soliton gases in integrable dispersive hydrodynamic systems. We first present a phenomenological approach based on the consideration of phase shifts in pairwise soliton collisions and leading to the kinetic…
A new integrable nonlocal nonlinear Schroedinger (NLS) equation with clear physical motivations is proposed. This equation is obtained from a special reduction of the Manakov system, and it describes Manakov solutions whose two components…
We propose an integrable model of a multicomponent spinor Bose-Einstein condensate in one dimension, which allows an exact description of the dynamics of bright solitons with spin degrees of freedom. We consider specifically an atomic…
Solitons play a fundamental role in dynamics of nonlinear excitations. Here we explore the motion of solitons in one-dimensional uniform Bose-Einstein condensates subjected to a spin-orbit coupling (SOC). We demonstrate that the spin…
Soliton gas or soliton turbulence is a subject of intense studies due to its great importance to optics, hydrodynamics, electricity, chemistry, biology and plasma physics. Usually, this term is used for integrable models where solitons…
An integrable model possessing inhomogeneous ground states is proposed as an effective model of non-uniform quantum condensates such as supersolids and Fulde--Ferrell--Larkin--Ovchinnikov superfluids. The model is a higher-order analog of…
We elaborate a mechanism for the formation of stable solitons of the semi-vortex type (with vorticities 0 and 1 in their two components), populating a finite bandgap in the spectrum of the spin-orbit-coupled binary Bose-Einstein condensate…
Spin-orbit (SO) coupling can be introduced in a Bose--Einstein condensate (BEC) as a gauge potential acting only in a localized spatial domain. Effect of such a SO "defect" can be understood by transforming the system to the integrable…
We investigate the Manakov model or, more generally, the vector nonlinear Schr\"odinger equation on the half-line. Using a B\"acklund transformation method, two classes of integrable boundary conditions are derived: mixed Neumann/Dirichlet…
Motion of curves and surfaces in $\R^3$ lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through…
The concept of soliton complex in a nonlinear dispersive medium is proposed. It is shown that strongly interacting identical topological solitons in the medium can form bound soliton complexes which move without radiation. This phenomenon…
The nonlinear Schrodinger equation supports solitons -- self-interacting, localized states that behave as nearly independent objects. We exhibit solitons with self-induced nonreciprocal dynamics in a discrete nonlinear Schrodinger equation.…
We consider the interaction of two-component bright-bright solitons with a narrow potential barrier (splitter) in the framework of a system of two Gross-Pitaevskii (nonlinear-Schr\"{o}dinger) equations modeling a binary Bose-Einstein…
We find one-, two-, and three-component solitons of the polar and ferromagnetic (FM) types in the general (non-integrable) model of a spinor (three-component) model of the Bose-Einstein condensate (BEC), based on a system of three…
Solitons and breathers are localized solutions of integrable systems that can be viewed as "particles'' of complex statistical objects called soliton and breather gases. In view of the growing evidence of their ubiquity in fluids and…
It was recently found that, under the action of the spin-orbit coupling (SOC) and Zeeman splitting (ZS), binary BEC with intrinsic cubic nonlinearity supports families of gap solitons, provided that the kinetic energy is negligible in…
We construct families of one-dimensional (1D) stable solitons in two-component $\mathcal{PT}$-symmetric systems with spin-orbit coupling (SOC) and quintic nonlinearity, which plays the critical role in 1D setups. The system models light…
We present the phase diagram, the underlying stability and magnetic properties as well as the dynamics of nonlinear solitary wave excitations arising in the distinct phases of a harmonically confined spinor $F=1$ Bose-Einstein condensate.…