Bright and Dark Solitons in a Periodically Attractive and Expulsive Potential with Nonlinearities Modulated in Space and Time

TL;DR

This paper investigates the existence and robustness of bright and dark solitons in a nonlinear Schrödinger equation with a periodically oscillating potential and spatially and temporally modulated nonlinearities.

Contribution

It introduces solutions for solitons in a complex, time-varying potential with modulated nonlinearities, demonstrating their stability despite periodic expulsive behavior.

Findings

Bright and dark solitons can exist in oscillating potentials.

Solitons remain robust despite periodic expulsive potential.

The study broadens understanding of soliton behavior in dynamic environments.

Abstract

This work deals with soliton solutions of the nonlinear Schroedinger equation with a diversity of nonlinearities. We solve the equation in a potential which oscillates in time between attractive and expulsive behavior, in the presence of nonlinearities which are modulated in space and time. Despite the presence of the periodically expulsive behavior of the potential, the results show that the nonlinear equation can support a diversity of localized excitations of the bright and dark type which are remarkably robust.