聚焦 Kundu-Eckhaus 方程中畸形波的奇异动力学行为研究

摘要/Abstract

摘要：

该文基于 Darboux 变换的相关结果, 利用变量分离法推导出了聚焦 Kundu-Eckhaus 方程的一般高阶畸形波解. 然后通过一些图形详细地讨论了这些畸形波解的动力学行为. 特别地, 这里可以观察到一个四瓣形畸形波和三眼形畸形波是可以共存的, 这是完全不同于之前存在的四眼形畸形波. 研究结果表明, 该文所研究的畸形波结构比在著名的非线性 Schrödinger 方程中的畸形波结构更为丰富.

关键词: 聚焦 Kundu-Eckhaus 方程, 变量分离方法, 畸形波

Abstract:

In this work, based on Darboux transformation general higher-order freak wave solutions of the focusing Kundu-Eckhaus equation are derived by using the variable separation method. Then the dynamics of these freak wave solutions are discussed with some graphics. In particular, we observe that one four-petaled freak wave and three eye-shaped ones can coexist, in contrast to the four eye-shaped ones reported before. They demonstrate that the structure of freak waves in this paper is richer than that in the well-known nonlinear Schrödinger equation.

Key words: The focusing Kundu-Eckhaus equation, The variable separation method, Freak waves

中图分类号:

O175.2

王秀彬, 田守富. 聚焦 Kundu-Eckhaus 方程中畸形波的奇异动力学行为研究[J]. 数学物理学报, 2023, 43(3): 785-794.

Wang Xiubin, Tian Shoufu. Exotic Dynamics of Freak Waves in the Focusing Kundu-Eckhaus Equation[J]. Acta mathematica scientia,Series A, 2023, 43(3): 785-794.

图/表 4

图 1

图 2

图 3

图 4

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