Mapping Between Generalized Nonlinear Schroedinger Equations and Neutral Scalar Field Theories and New Solutions of the Cubic-Quintic NLS Equation

TL;DR

This paper establishes a mapping between generalized nonlinear Schrödinger equations and scalar field theories, enabling the derivation of new breather solutions for the cubic-quintic NLS equation and analyzing their stability.

Contribution

It introduces a novel connection between NLS equations and scalar field theories, leading to new solutions and stability insights.

Findings

New moving breather solutions for cubic-quintic NLS

Numerical stability analysis of stationary solutions

Confirmation of stability results through dynamical evolution

Abstract

We highlight an interesting mapping between the moving breather solutions of the generalized Nonlinear Schrodinger (NLS) equations and the static solutions of neutral scalar field theories. Using this connection, we then obtain several new moving breather solutions of the cubic-quintic NLS equation both with and without uniform phase in space. The stability of some stationary solutions is investigated numerically and the results confirmed via dynamical evolution.