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In the Skyrme model atomic nuclei are modelled as quantized soliton solutions in a nonlinear field theory of pions. The mass number is given by the conserved topological charge $B$ of the solitons. Conventionally, Skyrmions are…
We investigate quasi-particle excitation modes and the topological number of a fractional-flux quantum vortex in a layered (multi-component) superconductor. The Bogoliubov equation for a half-flux quantum vortex is solved to show that there…
Stable vortex N-omers are constructed in coherently coupled N-component Bose-Einstein condensates. We classify all possible N-omers in terms of the mathematical graph theory and numerically construct all graphs for N=2,3,4. We also find…
Using the generalized perturbation reduction method the scalar nonlinear Schr\"odinger equation is transformed to the coupled nonlinear Schr\"odinger equations for auxiliary functions. A solution in the form of a two-component vector…
We consider possibilities to control dynamics of solitons of two types, maintained by the combination of cubic attraction and spin-orbit coupling (SOC) in a two-component system, namely, semi-dipoles (SDs) and mixed modes (MMs), by making…
On the basis of a recently-proposed method to find solitary solutions of generalized nonlinear Schrodinger equations [1]-[3], the existence of an envelope solitonlike solutions of a nonlinear Schrodinger equation containing an anti-cubic…
In this paper we consider a two component system of coupled non linear Schr\"odinger equations modeling the phase separation in the binary mixture of Bose-Einstein condensates and other related problems. Assuming the existence of solutions…
We consider dark solitons and their stability in spin-orbit coupled polariton condensates. The system supports spinor solitons of two types: conventional (symmetric) dark solitons and asymmetric half-dark solitons. They demonstrate…
We present semiclassical descriptions of Bose-Einstein condensates for configurations with spatial symmetry, e.g., cylindrical symmetry, and without any symmetry. The description of the cylindrical case is quasi-one-dimensional (Q1D), in…
We numerically simulate the creation process of two-dimensional skyrmionic excitations in antiferromagnetic spin-1 Bose--Einstein condensates by solving the full three-dimensional dynamics of the system from the Gross--Pitaevskii equation.…
We construct a variety of novel localized states with distinct topological structures in the 3D discrete nonlinear Schr{\"{o}}dinger equation. The states can be created in Bose-Einstein condensates trapped in strong optical lattices, and…
We study three distinct types of planar, spherically symmetric and localized structures, one of them having non-topological behavior and the two others being of topological nature. The non-topological structures have energy density…
Five-component minimum-energy bound states and mobile vector solitons of a spin-orbit-coupled quasi-one-dimensional hyperfine-spin-2 Bose-Einstein condensate are studied using the numerical solution and variational approximation of a…
Dynamics of solitons is considered in the framework of an extended nonlinear Schr\"odinger equation (NLSE), which is derived from a Zakharov-type model for wind-driven high-frequency (HF) surface waves in the ocean, coupled to damped…
Vortex-lattice structures of antiferromagnetic spinor Bose-Einstein condensates with hyperfine spin F=1 are investigated theoretically based on the Ginzburg-Pitaevskii equations near $T_{c}$. The Abrikosov lattice with clear core regions…
A concept of semiclassically concentrated solutions is formulated for the multidimensional nonlinear Schr\"odinger equation (NLSE) with an external field. These solutions are considered as multidimensional solitary waves. The center of mass…
We consider a class of multicomponent nonlinear Schrodinger equations (MNLS) related to the symmetric BD.I-type symmetric spaces. As important particular case of these MNLS we obtain the Kulish-Sklyanin model. Some new reductions and their…
Atomic-molecular Bose-Einstein condensates (BECs) offer brand new opportunities to revolutionize quantum gases and probe the variation of fundamental constants with unprecedented sensitivity. The recent realization of spin-orbit coupling…
We study the orbital stability and instability of single-spike bound states of semiclassical nonlinear Schrodinger (NLS) equations with critical exponent, linear and nonlinear optical lattices (OLs). These equations may model…
Dynamics of vector dark solitons in two-component Bose-Einstein condensates is studied within the framework of the coupled one-dimensional nonlinear Schr\"odinger (NLS) equations. We consider the small amplitude limit in which the coupled…