Solitary wave solutions of the Camassa–Holm-Nonlinear Schrödinger Equation

Abstract

This study investigates the solitary wave solutions to the defocusing nonlinear Schrödinger equation, which is known as Camassa–Holm-Nonlinear Schrödinger (CH-NLS) equation. The CH-NLS equation is newly derived in the sense of deformation of hierarchies structure of integrable systems. By implementing three different techniques, namely, the generalized (𝐺′∕𝐺)-expansion method, the new mapping method, and the modified simple equation method, the CH-NLS equation is solved analytically to find the exact solutions. As a result, various types of solitons such as dark, singular, and periodic solutions are obtained. The behaviors of some exact solutions are presented by figures.