{"title":"Riemann-Hilbert approach for the complex Sharma-Tasso-Olver equation with high-order poles","authors":"Mengdie Liu, Biao Li","doi":"10.1007/s12346-024-01053-5","DOIUrl":null,"url":null,"abstract":"<p>The inverse scattering transform is considered for the complex Sharma-Tasso-Olver equation with zero boundary condition by Riemann-Hilbert method. Under the reflection-less situation, we investigate the Riemann-Hilbert problem with one high-order pole and multiple high-order poles, respectively. By Laurent expansion of the Riemann-Hilbert problem and elimination of the integral factor involved in the solution, the explicit <i>N</i>-soliton solutions of the equation are derived. The interactions of several various solitons are displayed and their dynamics are analyzed.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-06-27","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/s12346-024-01053-5","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
The inverse scattering transform is considered for the complex Sharma-Tasso-Olver equation with zero boundary condition by Riemann-Hilbert method. Under the reflection-less situation, we investigate the Riemann-Hilbert problem with one high-order pole and multiple high-order poles, respectively. By Laurent expansion of the Riemann-Hilbert problem and elimination of the integral factor involved in the solution, the explicit N-soliton solutions of the equation are derived. The interactions of several various solitons are displayed and their dynamics are analyzed.
通过黎曼-希尔伯特方法，考虑了具有零边界条件的复 Sharma-Tasso-Olver 方程的反散射变换。在无反射情况下，我们分别研究了一个高阶极点和多个高阶极点的黎曼-希尔伯特问题。通过黎曼-希尔伯特问题的洛朗展开和消除解中涉及的积分因子，得出了方程的显式 N 孤子解。展示了几个不同孤子的相互作用，并分析了它们的动力学。
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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