{"title":"A Liouville integrable hierarchy with four potentials and its bi-Hamiltonian structure","authors":"MA WEN-XIU","doi":"10.59277/romrepphys.2023.75.115","DOIUrl":null,"url":null,"abstract":"\"We aim to construct a Liouville integrable Hamiltonian hierarchy from a specific matrix spectral problem with four potentials through the zero curvature formulation. The Liouville integrability of the resulting hierarchy is exhibited by a bi-Hamiltonian structure explored by using the trace identity. Illustrative examples of novel four-component coupled Liouville integrable nonlinear Schr¨odinger equations and modified Korteweg-de Vries equations are presented.\"","PeriodicalId":49588,"journal":{"name":"Romanian Reports in Physics","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Romanian Reports in Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.59277/romrepphys.2023.75.115","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 9
Abstract
"We aim to construct a Liouville integrable Hamiltonian hierarchy from a specific matrix spectral problem with four potentials through the zero curvature formulation. The Liouville integrability of the resulting hierarchy is exhibited by a bi-Hamiltonian structure explored by using the trace identity. Illustrative examples of novel four-component coupled Liouville integrable nonlinear Schr¨odinger equations and modified Korteweg-de Vries equations are presented."