Solitary waves of the two-dimensional Camassa–Holm—nonlinear Schrödinger equation

Abstract

In this work, we study solitary waves in a -dimensional variant of the defocusing nonlinear Schrödinger (NLS) equation, the so-called Camassa–Holm-NLS (CH-NLS) equation. We use asymptotic multiscale expansion methods to reduce this model to a Kadomtsev–Petviashvili (KP) equation. The KP model includes both the KP-I and KP-II versions, which possess line and lump soliton solutions. Using KP solitons, we construct approximate solitary wave solutions on top of the stable continuous-wave solution of the original CH-NLS model, which are found to be of both the dark and anti-dark type. We also use direct numerical simulations to investigate the validity of the approximate solutions, study their evolution, as well as their head-on collisions.