Backlund transformation,infinite number of conservation laws and fission properties of an integro-differential model for ocean internal solitary waves  

作　　者：Di Yu Zong-Guo Zhang Huan-He Dong Hong-Wei Yang 

机构地区：[1]College of Mathematics and System Science,Shandong University of Science and Technology,Qingdao 266590,China [2]School of Mathematics and Statistics,Qilu University of Technology(Shandong Academy of Sciences),Jinan,250353,China

出　　处：《Communications in Theoretical Physics》2021年第3期36-42,共7页理论物理通讯（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.11975143);the Nature Science Foundation of Shandong Province of China(Grant No.ZR2018MA017);the Taishan Scholars Program of Shandong Province,China(Grant No.ts20190936);the Shandong University of Science and Technology Research Fund,China(Grant No.2015TDJH102).

摘　　要：This paper presents an analytical investigation of the propagation of internal solitary waves in the ocean of finite depth.Using the multi-scale analysis and reduced perturbation methods,the integro-differential equation is derived,which is called the intermediate long wave(ILW)equation and can describe the amplitude of internal solitary waves.It can reduce to the Benjamin-Ono equation in the deep-water limit,and to the KdV equation in the shallow-water limit.Little attention has been paid to the features of integro-differential equations,especially for their conservation laws.Here,based on Hirota bilinear method,Backlund transformations in bilinear form of ILW equation are derived and infinite number of conservation laws are given.Finally,we analyze the fission phenomenon of internal solitary waves theoretically and verify it through numerical simulation.All of these have potential value for the further research on ocean internal solitary waves.

关 键 词：infinite conservation laws the integro-differential equation internal solitary waves fission properties of waves 

分 类 号：P731.24[天文地球—海洋科学] O175.6[理学—数学]