Solitons, breathers and rogue waves of the coupled Hirota system with 4×4 Lax pair

摘要

Solitons, breathers and rogue waves of the coupled Hirota system are investigated. To obtain these solutions, we construct the 4 x 4 Lax pair and Darboux transformation (DT). With zero backgrounds, we derive the one- and two-peak solitons. With non-zero and mixed backgrounds, we produce a family of the breather solutions and rational solutions for the purpose of describing the rogue waves. The second-order rogue-wave solutions on the mixed backgrounds are obtained. The existence and properties of bright-dark breathers and rogue waves are discussed. By adjusting the parameters in DT, we show the conversions between the bright breathers/rogue waves and the dark breathers/rogue waves in the course of evolution. We note that for such system if there is the modulation instability, it is of baseband type only. (C) 2019 Elsevier B.V. All rights reserved.