Nongauge bright soliton of the nonlinear Schrodinger (NLS) equation and a family of generalized NLS equations

TL;DR

This paper introduces a nongauge bright soliton solution for the nonlinear Schrödinger equation by adding a constant potential, and constructs a family of generalized NLS equations with solitonic solutions, establishing links with other nonlinear equations.

Contribution

It presents a novel nongauge bright soliton approach and develops a family of generalized NLS equations with exact solutions, connecting them to classical nonlinear equations.

Findings

Nongauge bright soliton solution depends only on the traveling variable.

Generalized NLS equations admit sech^p solitonic solutions.

Equivalence established with Korteveg-de Vries and Benjamin-Bona-Mahony equations for p=2.

Abstract

We present an approach to the bright soliton solution of the NLS equation from the standpoint of introducing a constant potential term in the equation. We discuss a `nongauge' bright soliton for which both the envelope and the phase depend only on the traveling variable. We also construct a family of generalized NLS equations with solitonic sech^p solutions in the traveling variable and find an exact equivalence with other nonlinear equations, such as the Korteveg-de Vries and Benjamin-Bona-Mahony equations when p=2