Doubly-Periodic Solutions of the Class I Infinitely Extended Nonlinear Schrodinger Equation

TL;DR

This paper introduces a class of doubly-periodic solutions for an extended nonlinear Schrödinger equation, featuring multiple free parameters that enable flexible wave pattern modeling in nonlinear wave evolution.

Contribution

It provides the first general doubly-periodic solutions with arbitrary higher-order terms and free parameters for the extended nonlinear Schrödinger equation.

Findings

Solutions have adjustable periods along two axes.

The solutions include many particular cases.

Potential applications in nonlinear wave evolution modeling.

Abstract

We present doubly-periodic solutions of the infinitely extended nonlinear Schrodinger equation with an arbitrary number of higher-order terms and corresponding free real parameters. Solutions have one additional free variable parameter that allows to vary periods along the two axes. The presence of infinitely many free parameters provides many possibilities in applying the solutions to nonlinear wave evolution. Being general, this solution admits several particular cases which are also given in this work.