Related papers: A bound state attractor in optical turbulence
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…
We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time(PT )-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave…
As is known, a solitary pulse in the complex cubic Ginzburg-Landau (GL) equation is unstable. We demonstrate that a system of two linearly coupled GL equations with gain and dissipation in one subsystem and pure dissipation in another…
We consider in detail the self-trapping of a soliton from a wave pulse that passes from a defocussing region into a focussing one in a spatially inhomogeneous nonlinear waveguide, described by a nonlinear Schrodinger equation in which the…
We report localized and unidirectional nonlinear traveling edge waves discovered theoretically and numerically in a 2D mechanical (phononic) topological insulator. The lattice consists of a collection of pendula with weak Duffing…
We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schroedinger equation under the influence of a small correction to the…
In this paper we study a system of coupled nonlinear Schrodinger equations modelling a quantum degenerate mixture of bosons and fermions. We analyze the stability of plane waves, give precise conditions for the existence of solitons and…
Nonlinear interactions in focusing media between traveling solitons and the dispersive shocks produced by an initial discontinuity are studied using the one-dimensional nonlinear Schrodinger equation. It is shown that, when solitons travel…
In this paper we deal with a nonlinear Schr\"{o}dinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
We develop a general analytical framework for determining the probability distribution of random nonlinear wave fields governed by the focusing nonlinear Schr\"odinger equation (fNLSE) in regimes where typical realizations are dominated by…
Using numerical modeling investigated interaction of solitary waves (solitons) of the regularized long wave equation. For reception the stable model of the nonlinear medium are used methods of the linear prediction and progressive…
An exact analytical model of the process of collision and nonlinear interaction of gravitational and/or electromagnetic soliton wave and strong non-soliton electromagnetic traveling wave of arbitrary profile propagating in the expanding…
We investigate the formation and interaction of solitons in the non-integrable Ostrovsky equation characterized by anomalous (positive) dispersion. This equation is relevant for describing wave phenomena in various media, including plasma,…
At the lower edge of the energy continuum the birth of an isolated quantum bound state is studied as caused by an infinitesimally small change of the interaction. In our model a single, asymptotically free massive quantum particle is…
In this work, inverse scattering transform for the sixth-order nonlinear Schr\"{o}dinger equation with both zero and nonzero boundary conditions at infinity is given, respectively. For the case of zero nonzero boundary conditions, in terms…
It has been established for some time that high-power pump can trap a probe beam of lower intensity that is simultaneously propagating in a Kerr-type optical medium, inducing a focusing of the probe with the emergence of modes displaying…
The stability properties and perturbation-induced dynamics of the full set of stationary states of the nonlinear Schroedinger equation are investigated numerically in two physical contexts: periodic solutions on a ring and confinement by a…
We consider the undamped nonlinear Schr\"odinger equation driven by a periodic external force. Classes of travelling solitons and multisoliton complexes are obtained by the numerical continuation in the parameter space. Two previously known…
Solitons are universal nonlinear excitations that appear in settings as varied as optics, water waves, and quantum gases [1-5]. While reduced models of soliton dynamics are well established, their validity and dynamical behaviour in…