动力系统(2+1)维变系数GKP方程的孤波解

Q1 Mathematics Chaos, Solitons and Fractals: X Pub Date : 2022-06-01 DOI:10.1016/j.csfx.2021.100069

Zhen ZHAO , Jing PANG

{"title":"动力系统(2+1)维变系数GKP方程的孤波解","authors":"Zhen ZHAO , Jing PANG","doi":"10.1016/j.csfx.2021.100069","DOIUrl":null,"url":null,"abstract":"<div><p>At present, the solution and qualitative analysis of nonlinear partial differential equations occupy a very important position in the study of dynamics. In this paper, the bilinear Bäcklund transformation of the (2+1)-dimensional variable-coefficient <span><math><mrow><mi>G</mi><mi>a</mi><mi>r</mi><mi>d</mi><mi>n</mi><mi>e</mi><mi>r</mi><mo>−</mo><mi>K</mi><mi>P</mi><mo>(</mo><mi>G</mi><mi>K</mi><mi>P</mi><mo>)</mo></mrow></math></span> equation is deduced by virtue of Hirota bilinear form, which consists of seven bilinear equations and involves ten arbitrary parameters. On the basis of the bilinear Bäcklund transformation, the traveling wave solution of the equation is obtained. Then the test function of the interaction solution of the positive quadratic function and exponential function of the (2+1)-dimensional variable-coefficient <span><math><mrow><mi>G</mi><mi>K</mi><mi>P</mi></mrow></math></span> equation is constructed, and then the test function of the positive quadratic function, hyperbolic cosine function and the interaction solution of the cosine function is constructed. With the help of mathematical symbol software Maple and Mathematica, the solitary wave solutions of (2+1)-dimensional variable-coefficient <span><math><mrow><mi>G</mi><mi>K</mi><mi>P</mi></mrow></math></span> equation is obtained by using Maple and Mathematica, and the interaction phenomena between a Lump wave and a Kink wave, a Lump wave and Multi-Kink waves are discussed.</p></div>","PeriodicalId":37147,"journal":{"name":"Chaos, Solitons and Fractals: X","volume":"8 ","pages":"Article 100069"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590054421000142/pdfft?md5=13c67829da3df92fe85d3f9ec17ee478&pid=1-s2.0-S2590054421000142-main.pdf","citationCount":"1","resultStr":"{\"title\":\"Solitary wave solutions of GKP equation with (2+1)dimensional variable-coefficients in dynamic systems\",\"authors\":\"Zhen ZHAO , Jing PANG\",\"doi\":\"10.1016/j.csfx.2021.100069\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>At present, the solution and qualitative analysis of nonlinear partial differential equations occupy a very important position in the study of dynamics. In this paper, the bilinear Bäcklund transformation of the (2+1)-dimensional variable-coefficient <span><math><mrow><mi>G</mi><mi>a</mi><mi>r</mi><mi>d</mi><mi>n</mi><mi>e</mi><mi>r</mi><mo>−</mo><mi>K</mi><mi>P</mi><mo>(</mo><mi>G</mi><mi>K</mi><mi>P</mi><mo>)</mo></mrow></math></span> equation is deduced by virtue of Hirota bilinear form, which consists of seven bilinear equations and involves ten arbitrary parameters. On the basis of the bilinear Bäcklund transformation, the traveling wave solution of the equation is obtained. Then the test function of the interaction solution of the positive quadratic function and exponential function of the (2+1)-dimensional variable-coefficient <span><math><mrow><mi>G</mi><mi>K</mi><mi>P</mi></mrow></math></span> equation is constructed, and then the test function of the positive quadratic function, hyperbolic cosine function and the interaction solution of the cosine function is constructed. With the help of mathematical symbol software Maple and Mathematica, the solitary wave solutions of (2+1)-dimensional variable-coefficient <span><math><mrow><mi>G</mi><mi>K</mi><mi>P</mi></mrow></math></span> equation is obtained by using Maple and Mathematica, and the interaction phenomena between a Lump wave and a Kink wave, a Lump wave and Multi-Kink waves are discussed.</p></div>\",\"PeriodicalId\":37147,\"journal\":{\"name\":\"Chaos, Solitons and Fractals: X\",\"volume\":\"8 \",\"pages\":\"Article 100069\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S2590054421000142/pdfft?md5=13c67829da3df92fe85d3f9ec17ee478&pid=1-s2.0-S2590054421000142-main.pdf\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chaos, Solitons and Fractals: X\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2590054421000142\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos, Solitons and Fractals: X","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2590054421000142","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 1

摘要

目前，非线性偏微分方程的求解和定性分析在动力学研究中占有十分重要的地位。本文利用Hirota双线性形式，推导了(2+1)维变系数Gardner−KP(GKP)方程的双线性Bäcklund变换，该方程由7个双线性方程组成，涉及10个任意参数。在双线性Bäcklund变换的基础上，得到了方程的行波解。然后构造(2+1)维变系数GKP方程的正二次函数与指数函数相互作用解的检验函数，然后构造正二次函数、双曲余弦函数与余弦函数相互作用解的检验函数。利用数学符号软件Maple和Mathematica，得到了(2+1)维变系数GKP方程的孤波解，并讨论了块波与扭结波、块波与多扭结波的相互作用现象。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Solitary wave solutions of GKP equation with (2+1)dimensional variable-coefficients in dynamic systems

At present, the solution and qualitative analysis of nonlinear partial differential equations occupy a very important position in the study of dynamics. In this paper, the bilinear Bäcklund transformation of the (2+1)-dimensional variable-coefficient $G a r d n e r - K P (G K P)$ equation is deduced by virtue of Hirota bilinear form, which consists of seven bilinear equations and involves ten arbitrary parameters. On the basis of the bilinear Bäcklund transformation, the traveling wave solution of the equation is obtained. Then the test function of the interaction solution of the positive quadratic function and exponential function of the (2+1)-dimensional variable-coefficient $G K P$ equation is constructed, and then the test function of the positive quadratic function, hyperbolic cosine function and the interaction solution of the cosine function is constructed. With the help of mathematical symbol software Maple and Mathematica, the solitary wave solutions of (2+1)-dimensional variable-coefficient $G K P$ equation is obtained by using Maple and Mathematica, and the interaction phenomena between a Lump wave and a Kink wave, a Lump wave and Multi-Kink waves are discussed.