Dynamics of breathers and rogue waves for a generalized discrete Hirota equation

Under investigation in this paper is a generalized discrete Hirota equation. Based on Lax pair, the Nth-fold Darboux transformation is constructed. The one- and two-breather solutions are obtained and analyzed. The first- and second-order rogue wave solutions are derived and investigated. The influences of parameters for solutions are discussed. In particular, the different structures of second-order rogue wave are observed. Moreover, the interaction solutions between rogue wave and one breather are constructed and studied.

Automated summary

This paper investigates a generalized discrete Hirota equation and constructs the Nth-fold Darboux transformation based on Lax pair. It obtains and analyzes the solutions for one- and two-breathers. The first- and second-order rogue wave solutions are derived and investigated, including discussion on the influences of parameters. Additionally, the interaction solutions between rogue wave and one breather are constructed and studied.