Darboux transformation for T-symmetric nonlocal complex modified Korteweg-de Vries system of equations

Abstract

onlinear partial differential equations are widely used as models to describe physical phenomena in various fields of sciences such as fluid mechanics, solid-state physics, plasma physics, chemical physics, condensed matter physics, optical fibers, biology, and geochemistry. One of the nonlinear partial differential equations is the complex modified Korteweg-de Vries equation. This equation has been proposed as a model for the nonlinear evolution of plasma waves and is the physical model that incorporates the propagation of transverse waves in a molecular chain model, and in a generalized elastic solid. In this paper, we study the T-symmetry nonlocal complex modified Korteweg-de Vries system of equations. This nonlocal system is obtained by Ablowitz-Musslimani type of reduction and is respectively T-symmetric nonlocal cmKdV system of equations. The Ablowitz - Musslimani type of reductions arises from remarkably simple symmetry reductions of general AKNS scattering problems. The method of the Darboux transformation is applied to obtain exact solutions.