{"title":"流体中 $$(3+1)$-dimensional 可变系数 Kadomtsev-Petviashvili 类方程的双线性形式、自贝克隆变换和扭结解","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":"{\"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}","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
摘要
流体力学与大气科学、海洋学和天体物理学等众多学科息息相关。在本文中,我们将注意力集中在流体中的((3+1)\)维变系数 Kadomtsev-Petviashvili 类方程上。通过 Hirota 方法,我们导出了双线性形式。我们得到了基于截断 Painlev\(\acute\textrm{e}}\) 展开的自动贝克隆变换和基于双线性形式的双线性贝克隆变换。以变量系数 \(\α (t)\), \(\beta (t)\), \(\gamma (y,t)\), \(\delta (t)\) 和 \(\mu (t)\) 作为特定的约束条件,给出了一扭结解和二扭结解。根据一结解,我们把 \(\gamma (y,t)\) 作为 y 的线性函数和三角函数,然后给出环型和周期型一结波,其中 t 和 y 为自变量。根据二扭结解,我们得到抛物型、线性型和周期型扭结波。
Bilinear form, auto-Bäcklund transformations and kink solutions of a \((3+1)\)-dimensional variable-coefficient Kadomtsev-Petviashvili-like equation in a fluid
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.