Rogue-wave and breather solutions of the Fokas-Lenells equation on theta-function backgrounds
Rogue-wave and breather solutions of the Fokas-Lenells equation on theta-function backgrounds
复制标题
DOI：
10.1016/j.aml.2023.108661
复制
发表时间：
2023-03
期刊：
影响因子：
--
通讯作者：
Ruomeng Li;Jingru Geng;X. Geng
中科院分区：
文献类型：
--
作者：
Ruomeng Li;Jingru Geng;X. Geng
本文发展了一种系统的方法，得到了θ函数背景下Fokas-Lenells方程的局域波解。首先，利用θ函数的性质，我们找到了Fokas-Lenells方程的θ函数种子解。其次，基于Lax对的Riccati方程，构造了Fokas-Lenells方程的Darboux变换。然后，利用代数几何方法中的Baker-Akhiezer函数，求解了具有θ函数势的Kaup-Newell型谱问题.最后，利用导出的Darboux变换和Baker-Akhiezer函数，构造了θ函数背景下Fokas-Lenells方程的精确Rogue波解和呼吸子解.此外，通过选择适当的参数，分析了各种局域波解的相互作用动力学。
A systematic method is developed to obtain localized wave solutions of the Fokas–Lenells equation on theta-function backgrounds. First, using the properties of the theta-functions, we find a theta-function seed solution of the Fokas–Lenells equation. Next, based on the Riccati equation of Lax pair, we construct a Darboux transformation of the Fokas–Lenells equation. Then, the Kaup–Newell type spectral problem with theta-function potentials is solved by using the Baker–Akhiezer functions in the algebro-geometric method. Finally, Exact rogue-wave and breather solutions of the Fokas–Lenells equation on theta-function backgrounds are constructed by using the derived Darboux transformation and Baker–Akhiezer functions. In addition, the interaction dynamics of various localized wave solutions are analyzed by choosing appropriate parameters.