Nonlinear Schrodinger equation with chaotic, random, and nonperiodic nonlinearity

TL;DR

This paper investigates the behavior of solitons in a nonlinear Schrödinger equation with chaotic, random, and nonperiodic cubic nonlinearity, exploring their evolution and robustness under complex perturbations relevant to physical systems.

Contribution

It introduces a study of soliton dynamics in a nonlinear Schrödinger equation with complex, nonperiodic nonlinearities, highlighting the effects of random perturbations on soliton stability.

Findings

Solitons exhibit robustness under chaotic and random nonlinear perturbations.

Random perturbations influence the transport and collective excitations in Bose-Einstein Condensates.

The study links nonlinear perturbations to physical phenomena like impurities and thermal effects.

Abstract

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 coordinates and to check its robustness under these conditions. Comparing with a real system, the perturbation can be related to, e.g., impurities in crystalline structures, or coupling to a thermal reservoir which, on the average, enhances the nonlinearity. We also discuss the relevance of such random perturbations to the dynamics of Bose-Einstein Condensates and their collective excitations and transport.