Related papers: Polarized solitons in a cubic-quintic medium
We study the strong instability of standing waves for a system of nonlinear Schr\"odinger equations with quadratic interaction under the mass resonance condition in dimension $d=5$.
We consider two-component nonlinear dissipative spatially extended systems of reaction-cross-diffusion type. Previously, such systems were shown to support "quasi-soliton" pulses, which have fixed stable structure but can reflect from…
Management of solitons in media with competing quadratic and cubic nonlinearities is investigated. Two schemes, using rapid modulations of a mismatch parameter, and of the Kerr nonlinearity parameter are studied. For both cases, the…
We consider the coupled propagation of an optical field and its second harmonic in a quadratic nonlinear medium governed by a coupled system of Schrodinger equations. We prove the existence of ring-profiled optical vortex solitons appearing…
The statics and dynamics of a stable, mobile three-dimensional (3D) spatiotemporal vortex light bullet in a cubic-quintic nonlinear medium with a focusing cubic nonlinearity above a critical value and any defocusing quintic nonlinearity is…
We studied the characteristics, regions of existence and stability of different types of solitons for a distributed model of a mode-locked laser whose dispersion is purely quartic and normal. Among the different types of solitons, we…
A brief review is given of some well-known and some very recent results obtained in studies of two- and three-dimensional (2D and 3D) solitons. Both zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are considered.…
Spatial solitons can exist in various kinds of nonlinear optical resonators with and without amplification. In the past years different types of these localized structures such as vortices, bright, dark solitons and phase solitons have been…
We report results of systematic numerical analysis of collisions between two and three stable dissipative solitons in the two-dimensional (2D) complex Ginzburg- Landau equation (CGLE) with the cubic-quintic (CQ) combination of gain and loss…
We study the influence of long-range interatomic interactions on the properties of supersonic pulse solitons in anharmonic chains. We show that in the case of ultra-long-range (e.g., screened Coulomb) interactions three different types of…
We consider soliton solutions of a two-dimensional nonlinear system with the self-focusing nonlinearity and a quasi-1D confining potential, taking harmonic potential as an example. We investigate a single soliton in detail and find…
By identifying the similarities between the coupled-wave equations and the parametrically driven nonlinear Schr\"odinger equation, we unveil the existence condition of the quadratic soliton mode-locked degenerate optical parametric…
We theoretically demonstrate the possibility to tune the temporal waveform of optical unipolar pulses upon their coherent interaction with a multi-level resonant medium. This is achieved through the coherent control of the response of a…
A model consisting of a mixed Kuramoto - Sivashinsky - KdV equation, linearly coupled to an extra linear dissipative equation, is proposed. The model applies to the description of surface waves on multilayered liquid films. The extra…
In systems that exhibit a bistability between nonlinear traveling waves and the basic state, pairs of fronts connecting these two states can form localized wave pulses whose stability depends on the interaction between the fronts. We…
Using a functional renormalization group approach, we study interaction-driven instabilities in quadratic band crossing point two-orbital models in two dimensions, extending a previous study of Sun et al. [1]. The wavevector-dependence of…
We study the statics and dynamics of a binary dipolar Bose-Einstein condensate soliton for repulsive inter- and intraspecies contact interactions with the two components subject to different spatial symmetries $-$ distinct…
We introduce a one-dimensional system combining the $\mathcal{PT}$-symmetric complex periodic potential and the $\chi ^{(2)}$ (second-harmonic-generating) nonlinearity. The imaginary part of the potential, which represents spatially…
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 explore stability regions for solitons in the nonlinear Schrodinger equation with a spatially confined region carrying a combination of self-focusing cubic and septimal terms, with a quintic one of either focusing or defocusing sign.…