Cauchy Matrix Type Solutions for the Nonlocal Nonlinear Schrödinger Equation

Abstract

In this paper, we study some Cauchy matrix type solutions for the nonlocal nonlinear Schrodinger equations, including Cauchy matrix type multisoliton solutions and Cauchy matrix type Jordan block solutions. These solutions are obtained from the Cauchy matrix type solutions of Ablowitz–Kaup–Newell–Segur equation through nonlocal reduction. The reduction procedure developed in this paper can apply to other systems which have Cauchy matrix type solutions and admit local and nonlocal reductions.