Related papers: Rotating soliton solutions in nonlocal nonlinear m…
In the present paper we deal with nonlinear dynamics of microtubules (MTs). The structure and role of MTs in cells are explained. One model explaining MT dynamics is explained. Solutions of the crucial nonlinear differential equation depend…
We discuss exact multi-soliton solutions to integrable hierarchies on noncommutative space-times in diverse dimension. The solutions are represented by quasi-determinants in compact forms. We study soliton scattering processes in the…
We introduce multi-soliton sets in the two-dimensional medium with the second-harmonic-generating nonlinearity subject to spatial modulation in the form of a triangle of singular peaks. Various families of symmetric and asymmetric sets are…
We study large-amplitude, very oblique Alfv\'en waves at low $\beta$, with small gradient length scales, comparable to the ion inertial scale $d_i$. Such waves have large density fluctuations, and slight dispersion from finite-frequency and…
In the recent work "Non-reciprocal topological solitons in active metamaterials" (see arXiv:2312.03544v1), for an analytical understanding of the system under consideration, the authors derive an ordinary differential equation for the…
We obtain multi-soliton solutions of the time-dependent Bogoliubov-de Gennes equations or, equivalently, Gorkov equations that describe the dynamics of a fermionic condensate in the dissipationless regime. There are two kinds of solitons -…
We study the appearance of compacton-like solutions within the hydrodynamic-type model taking into account effects of spatial non-locality
Compaction in reactive porous media is modelled as a reaction-diffusion process with a moving boundary. Asymptotic analysis is used to find solutions for the coupled nonlinear compaction equations, and a traveling wave solution is obtained…
Solitary waves in one-dimensional periodic media are discussed employing the nonlinear Schr\"odinger equation with a spatially periodic potential as a model. This equation admits two families of gap solitons that bifurcate from the edges of…
We present a class of orthogonal non-regular in a sense of Kalnins and Miller (hence non-St\"ackel) coordinates which are R-separable in 3-dim. Helmholtz equation. One family of parametric surfaces consists of parallel Dupin cyclides, the…
Although most soliton research has traditionally considered dominant quadratic dispersion, the recent discovery of pure-quartic solitons has inspired analysis of soliton solutions with large higher orders of dispersion. Here we present…
We address the interactions between optical solitons in the system with longitudinally varying nonlocality degree and nonlinearity strength. We consider a physical model describing light propagation in nematic liquid crystals featuring a…
We put forward new properties of lattice solitons in materials and geometries where both, the linear refractive index and the nonlinearity are spatially modulated. We show that the interplay between linear and out-of-phase nonlinear…
We address the properties of two-dimensional surface solitons supported by the interface of a waveguide array whose nonlinearity is periodically modulated. When the nonlinearity strength reaches its minima at the points where the linear…
Polar solitons, i.e., solitonic waves accompanying asymmetry of geometry or phase, have garnered attention in polar systems, such as ferroelectric or magnetoelectric materials, where they play a critical role in topological transitions and…
Nonlocal quantum fluids emerge as dark-matter models and tools for quantum simulations and technologies. However, strongly nonlinear regimes, like those involving multi-dimensional self-localized solitary waves, are marginally explored for…
In this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we…
We consider several ways of how one could classify the various types of soliton solutions related to nonlinear evolution equations which are solvable by the inverse scattering method. In doing so we make use of the fundamental analytic…
We report the existence of persistently rotating azimuthons in media with self-focusing Kerr and absorption nonlinearities. The nonlinear loss is balanced by power influx from the peripheral reservoir stored in slowly decaying tails of the…
We review recent progress in the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry-Andre…