Solitons, breathers and rogue waves in the coupled nonlocal reverse-time nonlinear Schrödinger equations

Abstract

In this paper, we obtain the N-bright-bright soliton, N-dark-bright soliton, general N-breather and Nth-order semirational rogue wave solutions of the coupled nonlocal reverse-time nonlinear Schrödinger (NLS) equations by using the Darboux transformation and limit technique. It is demonstrated that these solutions can be globally bounded or collapsed with singularities. The elastic collisions of the bounded two-bright-bright solitons and two-dark-bright solitons are discussed through the asymptotic analysis method. The degenerate bounded or collapsing Akhmediev breather and Kuznetsov-Ma breather, and the bounded breather-soliton and breather-breather mixed waves are graphically shown. In particular, there exist degenerate bounded or collapsing rogue waves, bounded or collapsing rogue waves coexisting and interacting with dark-bright solitons or breathers in the coupled nonlocal reverse-time integrable models, most of which have no counterparts in the coupled local NLS equations. The modulation instability analysis concerning the plane-wave background is performed to illustrate the existence of rogue waves.