具有三次非线性的二分量峰值系统的光滑多孤子解

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-09-04 DOI:10.3842/sigma.2022.066

Nianhua Li, Q.P. Liu

{"title":"具有三次非线性的二分量峰值系统的光滑多孤子解","authors":"Nianhua Li, Q.P. Liu","doi":"10.3842/sigma.2022.066","DOIUrl":null,"url":null,"abstract":"We present a reciprocal transformation which links the Geng-Xue equation to a particular reduction of the first negative flow of the Boussinesq hierarchy. We discuss two reductions of the reciprocal transformation for the Degasperis-Procesi and Novikov equations, respectively. With the aid of the Darboux transformation and the reciprocal transformation, we obtain a compact parametric representation for the smooth soliton solutions such as multi-kink solutions of the Geng-Xue equation.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2022-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Smooth Multisoliton Solutions of a 2-Component Peakon System with Cubic Nonlinearity\",\"authors\":\"Nianhua Li, Q.P. Liu\",\"doi\":\"10.3842/sigma.2022.066\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a reciprocal transformation which links the Geng-Xue equation to a particular reduction of the first negative flow of the Boussinesq hierarchy. We discuss two reductions of the reciprocal transformation for the Degasperis-Procesi and Novikov equations, respectively. With the aid of the Darboux transformation and the reciprocal transformation, we obtain a compact parametric representation for the smooth soliton solutions such as multi-kink solutions of the Geng-Xue equation.\",\"PeriodicalId\":49453,\"journal\":{\"name\":\"Symmetry Integrability and Geometry-Methods and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2022-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Symmetry Integrability and Geometry-Methods and Applications\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.3842/sigma.2022.066\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symmetry Integrability and Geometry-Methods and Applications","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.3842/sigma.2022.066","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

我们提出了一个倒易变换，它将耿雪方程与Boussinesq层次的第一个负流的一个特殊约简联系起来。我们分别讨论了Degasperis-Procesi和Novikov方程的倒数变换的两个约简。借助于Darboux变换和互易变换，我们得到了耿雪方程的光滑孤立子解（如多扭结解）的一个紧致参数表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Smooth Multisoliton Solutions of a 2-Component Peakon System with Cubic Nonlinearity

We present a reciprocal transformation which links the Geng-Xue equation to a particular reduction of the first negative flow of the Boussinesq hierarchy. We discuss two reductions of the reciprocal transformation for the Degasperis-Procesi and Novikov equations, respectively. With the aid of the Darboux transformation and the reciprocal transformation, we obtain a compact parametric representation for the smooth soliton solutions such as multi-kink solutions of the Geng-Xue equation.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.