Rogue waves for the(2+1)-dimensional Myrzakulov–Lakshmanan-Ⅳ equation on a periodic background  

作　　者：Xiao-Hui Wang Zhaqilao 

机构地区：[1]College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China [2]Laboratory of Infinite-dimensional Hamiltonian System and Its algorithm Application,Hohhot 010022,China [3]Center for Applied Mathematical Science,Inner Mongolia,Hohhot 010022,China

出　　处：《Communications in Theoretical Physics》2024年第4期32-42,共11页理论物理通讯（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 12 361 052);the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant Nos. 2020LH01010, 2022ZD05);the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region (Grant No. NMGIRT2414);the Fundamental Research Funds for the Inner Mongolia Normal University, China (Grant No. 2022JBTD007);the Key Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application (Inner Mongolia Normal University), and the Ministry of Education (Grant Nos. 2023KFZR01, 2023KFZR02)

摘　　要：In this paper, the rogue wave solutions of the(2+1)-dimensional Myrzakulov–Lakshmanan(ML)-Ⅳ equation, which is described by five component nonlinear evolution equations, are studied on a periodic background. By using the Jacobian elliptic function expansion method, the Darboux transformation(DT) method and the nonlinearization of the Lax pair, two kinds of rogue wave solutions which are expressed by Jacobian elliptic functions dn and cn, are obtained.The relationship between these five kinds of potential is summarized systematically. Firstly, the periodic rogue wave solution of one potential is obtained, and then the periodic rogue wave solutions of the other four potentials are obtained directly. The solutions we find present the dynamic phenomena of higher-order nonlinear wave equations.

关 键 词：rogue waves on a periodic background (2+1)-dimensional Myrzakulov-Lakshmanan-IV equation Darboux transformation Jacobian elliptic function 

分 类 号：O175[理学—数学]