Hybrid rogue waves and breather solutions on the double-periodic background for the Kundu-DNLS equation

In this paper, by using Darboux transformation (DT) method and Taylor expansion method, a new nth-order determinant of the hybrid rogue waves and breathers solution on the double-periodic background of Kundu-DNLS equation is constructed when n is even. Breathers and rogue waves can be obtained from this determinant, respectively. Further, the hybrid rogue waves and breathers solutions on the different periodic background are given explicitly, including the single-periodic background, the double-periodic background and the plane wave background by selecting different parameters. In addition, the form of the obtained solutions is summarized.