Integrable Nonlocal Reductions

Abstract

We present some nonlocal integrable systems by using the Ablowitz–Musslimani nonlocal reductions. We first present all possible nonlocal reductions of nonlinear Schrodinger (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.