New Solutions of Coupled Nonlocal NLS and Coupled Nonlocal mKdV Equations

TL;DR

This paper presents new solutions for coupled nonlocal NLS and mKdV equations, compares them with local counterparts, and introduces novel solutions for local equations not applicable to nonlocal versions.

Contribution

It offers novel solutions for coupled nonlocal NLS and mKdV equations and compares them with local equations, also providing new local solutions absent in nonlocal forms.

Findings

New solutions for coupled nonlocal NLS and mKdV equations

Comparison between nonlocal and local solutions

Introduction of local solutions not found in nonlocal equations

Abstract

We provide several novel solutions of the coupled Ablowitz-Musslimani (AM) version of the nonlocal nonlinear Schr\"odinger (NLS) equation and the coupled nonlocal modified Korteweg-de Vries (mKdV) equations. In each case we compare and contrast the corresponding solutions of the relevant coupled local equations. Further, we provide new solutions of the coupled local NLS and the coupled local mKdV equations which are not the solutions of the corresponding nonlocal equations.