Hybrid structures of rogue waves and breathers for the coupled Hirota system with negative coherent coupling

Abstract

Hybrid waves play the significant parts in the nonlinear physical systems. In this work, we study the hybrid waves for the coupled Hirota system with negative coherent coupling. Firstly, based on the generalized Darboux transformation method, we derive the Nth-order hybrid wave solutions with two spectral parameters, which can describe the mth-order rogue waves and (N−M)th-order breathers. According to such solutions, we graphically illustrate the properties of the second-, third- and fourth-order hybrid waves. Moreover, we exhibit five kinds of hybrid structures consisting of the rogue waves and breathers: (i) consisting of the first-order rogue waves and first-order breathers; (ii) consisting of the second-order degenerate breathers; (iii) consisting of the first-order rogue waves and second-order degenerate breathers; (iv) consisting of the second-order rogue waves and first-order breathers; (v) consisting of the second-order rogue waves and second-order degenerate breathers. In addition, we show that the angle between the two-hump bright breathers and the negative direction of the -axis increases with the value of the real parameter in the coupled Hirota system with negative coherent coupling.