Bilinear form, auto-Bäcklund transformations and kink solutions of a \((3+1)\)-dimensional variable-coefficient Kadomtsev-Petviashvili-like equation in a fluid
{"title":"Bilinear form, auto-Bäcklund transformations and kink solutions of a \\((3+1)\\)-dimensional variable-coefficient Kadomtsev-Petviashvili-like equation in a fluid","authors":"Yu-Qi Chen, Bo Tian, Yuan Shen, Tian-Yu Zhou","doi":"10.1007/s12043-024-02740-3","DOIUrl":null,"url":null,"abstract":"<div><p>Fluid mechanics has been linked to a wide range of disciplines, such as atmospheric science, oceanography and astrophysics. In this paper, we focus our attention on a <span>\\((3+1)\\)</span>-dimensional variable-coefficient Kadomtsev-Petviashvili-like equation in a fluid. Through the Hirota method, we derive a bilinear form. We obtain an auto-Bäcklund transformation based on the truncated Painlev<span>\\(\\acute{\\textrm{e}}\\)</span> expansion and a bilinear Bäcklund transformation based on the bilinear form. With the variable coefficients <span>\\(\\alpha (t)\\)</span>, <span>\\(\\beta (t)\\)</span>, <span>\\(\\gamma (y,t)\\)</span>, <span>\\(\\delta (t)\\)</span> and <span>\\(\\mu (t)\\)</span> taken as certain constraints, one- and two-kink solutions are shown. Based on the one-kink solutions, we take <span>\\(\\gamma (y,t)\\)</span> as the linear and trigonometric functions of <i>y</i>, and then give the ring-type and periodic-type one-kink waves, where <i>t</i> and <i>y</i> are the independent variables. According to the two-kink solutions, we obtain the parabolic-type, linear-type and periodic-type kink waves.</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pramana","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s12043-024-02740-3","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: 0
Abstract
Fluid mechanics has been linked to a wide range of disciplines, such as atmospheric science, oceanography and astrophysics. In this paper, we focus our attention on a \((3+1)\)-dimensional variable-coefficient Kadomtsev-Petviashvili-like equation in a fluid. Through the Hirota method, we derive a bilinear form. We obtain an auto-Bäcklund transformation based on the truncated Painlev\(\acute{\textrm{e}}\) expansion and a bilinear Bäcklund transformation based on the bilinear form. With the variable coefficients \(\alpha (t)\), \(\beta (t)\), \(\gamma (y,t)\), \(\delta (t)\) and \(\mu (t)\) taken as certain constraints, one- and two-kink solutions are shown. Based on the one-kink solutions, we take \(\gamma (y,t)\) as the linear and trigonometric functions of y, and then give the ring-type and periodic-type one-kink waves, where t and y are the independent variables. According to the two-kink solutions, we obtain the parabolic-type, linear-type and periodic-type kink waves.
期刊介绍:
Pramana - Journal of Physics is a monthly research journal in English published by the Indian Academy of Sciences in collaboration with Indian National Science Academy and Indian Physics Association. The journal publishes refereed papers covering current research in Physics, both original contributions - research papers, brief reports or rapid communications - and invited reviews. Pramana also publishes special issues devoted to advances in specific areas of Physics and proceedings of select high quality conferences.