Solitons with Cubic and Quintic Nonlinearities Modulated in Space and Time

TL;DR

This paper investigates soliton solutions of the nonlinear Schrödinger equation with cubic and quintic nonlinearities, focusing on how space and time modulation of parameters influences the formation and behavior of localized nonlinear waves.

Contribution

It extends existing methods to solve the nonlinear Schrödinger equation with modulated nonlinearities and background, demonstrating control over soliton types and oscillations through parameter modulation.

Findings

Generated brightlike and darklike localized waves.

Showed oscillation behaviors driven by parameter modulation.

Provided a method to control soliton properties via space-time parameters.

Abstract

This work deals with soliton solutions of the nonlinear Schroedinger equation with cubic and quintic nonlinearities. We extend the procedure put forward in a recent Letter and we solve the equation in the presence of linear background, and cubic and quintic interactions which are modulated in space and time. As a result, we show how a simple parameter can be used to generate brightlike or darklike localized nonlinear waves which oscillate in several distinct ways, driven by the space and time dependence of the parameters that control the trapping potential, and the cubic and quintic nonlinearities.