{"title":"On a two-component Camassa–Holm equation","authors":"Zixin Zhang, Q.P. Liu","doi":"10.1016/j.aml.2025.109502","DOIUrl":null,"url":null,"abstract":"<div><div>A two-component generalization of the Camassa–Holm equation and its reduction proposed recently by Xue, Du and Geng [Appl. Math. Lett. <strong>146</strong> (2023) 108795] are studied. For this two-component equation, its missing bi-Hamiltonian structure is constructed and a Miura transformation is introduced so that it may be regarded as a modification of the very first two-component Camassa–Holm equation. Using a proper reciprocal transformation, a particular reduction of this two-component equation, which admits <span><math><mi>N</mi></math></span>-peakon solution, is shown to be a flow of the integrable hierarchy related to the celebrated Burgers equation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109502"},"PeriodicalIF":2.8000,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965925000527","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/2/18 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
A two-component generalization of the Camassa–Holm equation and its reduction proposed recently by Xue, Du and Geng [Appl. Math. Lett. 146 (2023) 108795] are studied. For this two-component equation, its missing bi-Hamiltonian structure is constructed and a Miura transformation is introduced so that it may be regarded as a modification of the very first two-component Camassa–Holm equation. Using a proper reciprocal transformation, a particular reduction of this two-component equation, which admits -peakon solution, is shown to be a flow of the integrable hierarchy related to the celebrated Burgers equation.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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