Abstract
In this paper, by using the Darboux transformation (DT) method and the Taylor expansion method, a new nth-order determinant of the hybrid rogue waves and breathers solution on the double-periodic background of the Kundu-DNLS equation is constructed when n is even. Breathers and rogue waves can be obtained from this determinant, respectively. Further to this, the hybrid rogue waves and breathers solutions on the different periodic backgrounds 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.
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