逆时空非局域Fokas-Lenells方程周期背景上的复合波解  

Hybrid Waves Solutions on the Periodic Background for the Nonlocal Reverse Space-Time Fokas-Lenells Equation

作　　者：赵一杰 扎其劳[1,2,3] ZHAO Yijie;Zhaqilao(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Inner Mongolia Center for Applied Mathematical Science,Hohhot 010022,China;Key Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application,Ministry of Education,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022 [2]内蒙古自治区应用数学中心,内蒙古呼和浩特010022 [3]无穷维哈密顿系统及其算法应用教育部重点实验室,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学版）》2024年第5期524-531,共8页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目“在周期背景上的怪波及其相关问题研究”(12361052);内蒙古自治区青年科技人才发展资助项目(创新团队)“应用数学团队”(NMGIRT2414);内蒙古师范大学基本科研业务费资助项目“应用数学创新团队建设项目”(2022JBTD007)。

摘　　要：利用达布变换方法,推导出逆时空非局域Fokas-Lenells方程周期背景上的复合波解。首先,利用Kaup-Newell Lax对,给出一重达布变换和N重达布变换的行列式表示。选取平面波解,得到kink型周期波、呼吸子、亮暗孤子及其复合波解。另外,构造了半退化达布变换,获得怪波、呼吸子及其复合波解。The hybrid wave solutions on the periodic background for the nonlocal reverse space-time Fokas-Lenells equation are derived by using Darboux transformation method in the paper.Firstly,the determinant representations of one-fold Darboux transformation and N-fold Darboux transformation are expressed by using the Kaup-Newell spectrum problem.And then,the kink-type periodic wave,the breather solutions,the light and dark soliton solutions,and hybrid wave solutions are obtained by selecting the plane wave solution.Furthermore,the solution of the rouge waves,the breathers and hybrid waves are obtained by constructing the semi-degenerate Darboux transformation.

关 键 词：周期背景上的怪波解 达布变换 半退化达布变换 

分 类 号：O175.29[理学—数学]