Eckhaus-Kundu方程的孤波解、周期波解及它们间的演化关系
Solitary and Periodic Wave Solutions of the Eckhaus-Kundu Equation and Their Evolutionary Relations
摘要: 该文结合定性分析方法和基于首次积分的分析法，探讨了Eckhaus-Kundu方程的孤波解、周期波解，以及上述二种解关于Hamilton系统能量的演化。本文求出了所研方程全部的钟状和扭状孤波解，并提出了新孤波解以及三类周期波解。通过本文的论述，发现了所研方程为什么能产生孤波解和周期波解，实质上是该方程解的振幅对应的Hamilton系统的能量变化起着关键的作用。
Abstract: In the paper, the solitary and periodic wave solutions of the Eckhaus-Kundu equation and their evolutionary relation with Hamilton energy are studied via combining qualitative analysis with an-alytical method on the basis of first integral. All bell-shaped and kink-shaped solitary wave solu-tions of the equation are obtained, and the new solitary wave solutions and three kinds of periodic wave solutions are given. The discussion reveals that the energy of Hamilton system, which takes different values, is the crucial factor for the emergence of solitary and periodic wave solutions to the studied equation, and the Hamilton system is corresponded by the amplitudes of these solutions.
文章引用：张雪, 郭玉立. Eckhaus-Kundu方程的孤波解、周期波解及它们间的演化关系[J]. 应用数学进展, 2022, 11(12): 8988-9003. https://doi.org/10.12677/AAM.2022.1112948

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