Application of the Dbar-method to a nonlocal coupled modified NLS equation and nonlocal reduction

Abstract

A nonlocal modified NLS (mNLS) equation is studied by using Dbar method and nonlocal reduction. The nonlocal coupled modified NLS (cmNLS) equation and its Lax representation are derived by introducing bi-Dbar problem and parity condition. The special spectral transform matrices are defined to get the solutions of nonlocal cmNLS equation. The general reduction conditions from the nonlocal cmNLS equation to the nonlocal mNLS equation are presented. As applications, some soliton solutions, breather solutions, periodic solutions and mixed solutions of the nonlocal mNLS equation are given.