Related papers: Solitons supported by complex PT symmetric Gaussia…
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of…
The existence, stability and other dynamical properties of a new type of multi-dimensional (2D or 3D) solitons supported by a transverse low-dimensional (1D or 2D, respectively) periodic potential in the nonlinear Schr\"{o}dinger equation…
We consider the existence and stability of solitons in generalized galileons, scalar field theories with higher-derivative interactions but second-order equations of motion. It has previously been proven that no stable, static solitons…
We study the bound states of two-dimensional bright solitons in nonlocal nonlinear media. The general properties and stability of these multisolitary structures are investigated analytically and numerically. We have found that a steady…
We address the existence and properties of multipole solitons localized at a thermally insulating interface between uniform or layered thermal media and a linear dielectric. We find that in the case of uniform media, only surface multipoles…
The stabilization of one-dimensional solitons by a nonlinear lattice against the critical collapse in the focusing quintic medium is a challenging issue. We demonstrate that this purpose can be achieved by combining a…
We present a brief overview of the basic concepts of the soliton stability theory and discuss some characteristic examples of the instability-induced soliton dynamics, in application to spatial optical solitons described by the NLS-type…
We demonstrate a robust, stable, mobile, two-dimensional (2D) spatial and three-dimensional (3D) spatiotemporal optical soliton in the core of an optical vortex, while all nonlinearities are of the cubic (Kerr) type. The 3D soliton can…
We predict the existence and address the stability of two-dimensional surface solitons featuring topologically complex shapes, including dipoles, vortices, and bound states of vortex solitons, at the interface of nonlocal thermal media.…
Solitons are self-reinforcing localized wave packets arising from a balance of linear and nonlinear effects. This definition encompasses the interplay of nonlinear gain and loss, leading to the concept of dissipative solitons that has been…
We demonstrate a stable, mobile, dipolar or nondipolar three-dimensional matter-wave soliton in the vortex core of a uniform nondipolar condensate. All intra- and inter-species contact interactions can be repulsive for a strongly dipolar…
Using the variational approximation(VA) and direct simulations, we find stable 2D and 3D solitons in the self-attractive Gross-Pitaevskii equation (GPE) with a potential which is uniform in one direction ($z$) and periodic in the others…
We study spatial and temporal solitons in the $\mathcal{PT}$ symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high- and low-frequency solitons are found to be completely determined by a single…
The existence of a novel type of solitons in periodic Kerr media constructed as superposition of noninteracting gap-solitons of different kinds (bright, dark and periodic) is first demonstrated. The periodic modulation of the nonlinearity…
We consider one- and two-dimensional (1D and 2D) optical or matter-wave media with a maximum of the local self-repulsion strength at the center, and a minimum at periphery. If the central area is broad enough, it supports ground states in…
In the present work, we numerically explore the existence and stability properties of different types of configurations of dark-bright solitons, dark-bright soliton pairs and pairs of dark-bright and dark solitons in discrete settings,…
We introduce a two-dimensional (2D) system, which can be implemented in dual-core planar optical couplers with the Kerr nonlinearity in its cores, making it possible to blend effects of the PT symmetry, represented by the balanced linear…
We address the properties and dynamical stability of one-dimensional vector lattice solitons in Kerr-type cubic medium with harmonic transverse modulation of refractive index. We discovered that unstable families of scalar lattice solitons…
We analyze the stability and dynamics of dissipative Kerr solitons in the presence of a parabolic potential. This potential stabilizes oscillatory and chaotic regimes, favoring the generation of static DKSs. Furthermore, the potential…
We present a unified theoretical study of the bright solitons governed by self-focusing and defocusing nonlinear Schrodinger (NLS) equations with generalized parity-time (PT)-symmetric Scarff II potentials. Particularly, a PT-symmetric…