Wide Localized Solitons in Systems with Time and Space-Modulated Nonlinearities

TL;DR

This paper develops a method using point canonical transformations to find wide localized soliton solutions in nonautonomous nonlinear Schrödinger equations with time and space-dependent nonlinearities, expanding the class of solvable models.

Contribution

It introduces a generalized approach to obtain explicit wide soliton solutions in complex nonautonomous nonlinear Schrödinger systems with variable nonlinearities and external potentials.

Findings

Derived explicit wide localized soliton solutions.

Extended the class of solvable nonautonomous nonlinear Schrödinger equations.

Generalized external trapping potentials and nonlinearities.

Abstract

In this work we apply point canonical transformations to solve some classes of nonautonomous nonlinear Schr\"{o}dinger equation namely, those which possess specific cubic and quintic - time and space dependent - nonlinearities. In this way we generalize some procedures recently published which resort to an ansatz to the wavefunction and recover a time and space independent nonlinear equation which can be solved explicitly. The method applied here allow us to find wide localized (in space) soliton solutions to the nonautonomous nonlinear Schr\"{o}dinger equation, which were not presented before. We also generalize the external potential which traps the system and the nonlinearities terms.