{"title":"In the Shallow Water: Auto-Bäcklund, Hetero-Bäcklund and Scaling Transformations via a (2+1)-Dimensional Generalized Broer-Kaup System","authors":"Xin-Yi Gao","doi":"10.1007/s12346-024-01025-9","DOIUrl":null,"url":null,"abstract":"<p>These days, watching the shallow water waves, people think about the nonlinear Broer-type models, e.g., a (2+1)-dimensional generalized Broer-Kaup system modeling, e.g., certain nonlinear long waves in the shallow water. For that system, with reference to, e.g., the wave height and wave horizontal velocity, this paper avails of symbolic computation to obtain (A) an auto-Bäcklund transformation with some solitons; (B) a group of the scaling transformations and (C) a group of the hetero-Bäcklund transformations, to a known linear partial differential equation, from that system. Results rely on the coefficients in that system</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12346-024-01025-9","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
These days, watching the shallow water waves, people think about the nonlinear Broer-type models, e.g., a (2+1)-dimensional generalized Broer-Kaup system modeling, e.g., certain nonlinear long waves in the shallow water. For that system, with reference to, e.g., the wave height and wave horizontal velocity, this paper avails of symbolic computation to obtain (A) an auto-Bäcklund transformation with some solitons; (B) a group of the scaling transformations and (C) a group of the hetero-Bäcklund transformations, to a known linear partial differential equation, from that system. Results rely on the coefficients in that system
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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