Integrable Nonlocal Reductions

TL;DR

This paper explores nonlocal integrable systems derived from classical equations using nonlocal reductions, providing new solutions and extending to super integrable equations.

Contribution

It systematically classifies nonlocal reductions of key integrable systems and introduces novel nonlocal super equations with explicit solutions.

Findings

Derived all nonlocal reductions of NLS and mKdV systems.

Constructed soliton solutions for these nonlocal equations.

Extended nonlocal reductions to super integrable systems, introducing new equations.

Abstract

We present some nonlocal integrable systems by using the Ablowitz-Musslimani nonlocal reductions. We first present all possible nonlocal reductions of nonlinear Schr\"{o}dinger (NLS) and modified Korteweg-de Vries (mKdV) systems. We give soliton solutions of these nonlocal equations by using the Hirota method. We extend the nonlocal NLS equation to nonlocal Fordy-Kulish equations by utilizing the nonlocal reduction to the Fordy-Kulish system on symmetric spaces. We also consider the super AKNS system and then show that Ablowitz-Musslimani nonlocal reduction can be extended to super integrable equations. We obtain new nonlocal equations namely nonlocal super NLS and nonlocal super mKdV equations.