{"title":"Completion of the Guo-Hierarchy Integrable Coupling with Self-Consistent Sources in a Nonlinear Wave System","authors":"Han-yu Wei, En-Gui Fan null, W. Ma","doi":"10.4208/eajam.200121.190921","DOIUrl":null,"url":null,"abstract":". Water waves are actively studied. A new method to generate new wave systems through making perturbation in matrix spectral problems for integrable couplings is presented, which is called the “completion process of integrable couplings”. As its ap-plication, we construct an integrable coupling hierarchy and show that each equation in the resulting hierarchy has a bi-Hamiltonian structure by taking use of the component-trace identity. Moreover, the self-consistent sources of integrable coupling is presented based on the theory of self-consistent sources.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"East Asian Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/eajam.200121.190921","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
. Water waves are actively studied. A new method to generate new wave systems through making perturbation in matrix spectral problems for integrable couplings is presented, which is called the “completion process of integrable couplings”. As its ap-plication, we construct an integrable coupling hierarchy and show that each equation in the resulting hierarchy has a bi-Hamiltonian structure by taking use of the component-trace identity. Moreover, the self-consistent sources of integrable coupling is presented based on the theory of self-consistent sources.
期刊介绍:
The East Asian Journal on Applied Mathematics (EAJAM) aims at promoting study and research in Applied Mathematics in East Asia. It is the editorial policy of EAJAM to accept refereed papers in all active areas of Applied Mathematics and related Mathematical Sciences. Novel applications of Mathematics in real situations are especially welcome. Substantial survey papers on topics of exceptional interest will also be published occasionally.