On rogue wave in the Kundu-DNLS equation

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• 作者：Shibao Shan ; Chuanzhong Li ; Jingsong He
• 关键词：Kundu-DNLS equation ; Darboux transformation ; Soliton solutions ; Breather solution ; Positon solution ; Rogue waves
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：2013
• 出版时间：December, 2013
• 年：2013
• 卷：18
• 期：12
• 页码：3337-3349
• 全文大小：2229 K

文摘

In this paper, the determinant representation of the n-fold Darboux transformation (DT) of the Kundu-DNLS equation is given. Based on our analysis, the soliton solutions, positon solutions and breather solutions of the Kundu-DNLS equation are given explicitly. Further, we also construct the rogue wave solutions which are given by using the Taylor expansion of the breather solution. Particularly, these rogue wave solutions possess several free parameters. With the help of these parameters, these rogue waves constitute several patterns, such as fundamental pattern, triangular pattern, circular pattern.