Exact solutions of the nonlocal complex modified Korteweg-de Vries system of equations

Abstract

To describe some physical process further, it becomes more and more important to find exact solutions and interactions among solutions of nonlinear wave solutions. In this paper,
we study the two-dimensional nonlocal complex modified Korteweg-de Vries system of equations obtained from Ablowitz–Kaup-Newell-Segur scheme by Ablowitz-Musslimani type nonlocal reductions. This system of equations admits a representation as the compatibility conditions. For the two-dimensional nonlocal complex modified Korteweg-de Vries system of equations, we use the technique of Darboux transformation, which provides an algebraic iterative algorithm to obtain a series of analytic solutions from a known. The derived solutions are soliton solutions when the seed solution is zero.