广义五阶非线性薛定谔方程的怪波与呼吸子的复合波解  

Hybrid Rogue Wave and Breather Solutions for the Generalized Fifth-order Nonlinear Schrödinger Equation

作　　者：董浩楠 扎其劳[1,2] DONG Haonan;Zhaqilao(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Inner Mongolia Center for Applied Mathematics,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

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2024年第1期38-43,52,共7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发展资助项目“应用数学”(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：基于规范变换,为广义五阶非线性薛定谔方程建立达布变换。应用达布变换的可迭代性质,获得该方程的N重达布变换。把广义五阶非线性薛定谔方程Lax对的两组特解代入二重和三重达布变换中,获得该方程的怪波与呼吸子的复合波解。研究表明怪波和呼吸子可以在复合波解中独立存在。Hybrid rogue wave and breather solutions for the generalized fifth-order nonlinear Schrödinger equation are investigated by extended Darboux transformation.Firstly,the Darboux transformation is constructed based on gauge transformation for the equation;and then,the N-fold Darboux transformation is derived by utilizing the iterative property of the Darboux transformation;finally,the hybrid rogue wave and breather solutions of the equation are obtained through substituting two sets of the particular solution for the Lax pair of the equation into two-fold and three-fold Darboux transformation.The results indicate that different parameters have different effects on hybrid solutions.As a novel result,rogue waves and breathers are able to exist independently on.

关 键 词：复合波解 广义五阶非线性薛定谔方程 达布变换 

分 类 号：O175.29[理学—数学]