Hybrid structures of the rogue waves and breather-like waves for the higher-order coupled nonlinear Schrödinger equations

Abstract

Under investigation in this paper is the higher-order coupled nonlinear Schrödinger system, which describe the ultrashort optical pulses in nonlinear medium. Based on Lax pair, choosing nonzero seed solutions, Nth-order hybrid solutions for the higher-order coupled nonlinear Schrödinger equations are constructed via the generalized Darboux transformation. The profile and energy distribution of three kinds of hybrid structures of the rogue waves and breather-like waves were exhibited: (I) the first-order rogue waves and one breather-like waves; (II) the second-order rogue waves and two breather-like waves; (III) the third-order rogue waves and three breather-like waves. In addition, the influences of parameters for the properties of hybrid structures are discussed.