$$(2+1)$$维扩展瓦赫年科-帕克斯方程中的分岔、游波解和动力学分析

IF 1.4 4区 物理与天体物理 Q2 MATHEMATICS, APPLIED Journal of Nonlinear Mathematical Physics Pub Date : 2024-06-04 DOI:10.1007/s44198-024-00202-3
Yan Sun, Juan-Juan Wu, Xiao-Yong Wen
{"title":"$$(2+1)$$维扩展瓦赫年科-帕克斯方程中的分岔、游波解和动力学分析","authors":"Yan Sun, Juan-Juan Wu, Xiao-Yong Wen","doi":"10.1007/s44198-024-00202-3","DOIUrl":null,"url":null,"abstract":"<p>This paper is concerned with the bifurcation of the traveling wave solutions, as well as the dynamical behaviors and physical property of the soliton solutions of the (2+1)-dimensional extended Vakhnenko–Parkes (eVP) equation. Firstly, based on the traveling wave transformation, the planar dynamical system corresponding to the (2+1)-dimensional eVP equation is derived, and then the singularity type and trajectory map of this system are obtained and analyzed. Based on the bifurcation of this system, the analytical expression for the periodic wave solution is given and shown graphically. Secondly, the <i>N</i>-soliton solutions are obtained via the bilinear method, and some important physical quantities and asymptotic analysis of one-soliton and two-soliton solutions are discussed. The results obtained in this paper might be useful for understanding the propagation of high-frequency waves.</p>","PeriodicalId":48904,"journal":{"name":"Journal of Nonlinear Mathematical Physics","volume":"68 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bifurcation, Traveling Wave Solutions and Dynamical Analysis in the $$(2+1)$$ -Dimensional Extended Vakhnenko–Parkes Equation\",\"authors\":\"Yan Sun, Juan-Juan Wu, Xiao-Yong Wen\",\"doi\":\"10.1007/s44198-024-00202-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper is concerned with the bifurcation of the traveling wave solutions, as well as the dynamical behaviors and physical property of the soliton solutions of the (2+1)-dimensional extended Vakhnenko–Parkes (eVP) equation. Firstly, based on the traveling wave transformation, the planar dynamical system corresponding to the (2+1)-dimensional eVP equation is derived, and then the singularity type and trajectory map of this system are obtained and analyzed. Based on the bifurcation of this system, the analytical expression for the periodic wave solution is given and shown graphically. Secondly, the <i>N</i>-soliton solutions are obtained via the bilinear method, and some important physical quantities and asymptotic analysis of one-soliton and two-soliton solutions are discussed. The results obtained in this paper might be useful for understanding the propagation of high-frequency waves.</p>\",\"PeriodicalId\":48904,\"journal\":{\"name\":\"Journal of Nonlinear Mathematical Physics\",\"volume\":\"68 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-06-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Nonlinear Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s44198-024-00202-3\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s44198-024-00202-3","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

摘要

本文主要研究(2+1)维扩展 Vakhnenko-Parkes (eVP)方程行波解的分岔以及孤子解的动力学行为和物理特性。首先,基于行波变换推导出(2+1)维 eVP 方程对应的平面动力系统,然后得到并分析了该系统的奇点类型和轨迹图。在该系统分岔的基础上,给出了周期波解的解析表达式,并以图形表示。其次,通过双线性方法得到了 N 个孤立子解,并讨论了单孤立子解和双孤立子解的一些重要物理量和渐近分析。本文获得的结果可能有助于理解高频波的传播。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

摘要图片

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Bifurcation, Traveling Wave Solutions and Dynamical Analysis in the $$(2+1)$$ -Dimensional Extended Vakhnenko–Parkes Equation

This paper is concerned with the bifurcation of the traveling wave solutions, as well as the dynamical behaviors and physical property of the soliton solutions of the (2+1)-dimensional extended Vakhnenko–Parkes (eVP) equation. Firstly, based on the traveling wave transformation, the planar dynamical system corresponding to the (2+1)-dimensional eVP equation is derived, and then the singularity type and trajectory map of this system are obtained and analyzed. Based on the bifurcation of this system, the analytical expression for the periodic wave solution is given and shown graphically. Secondly, the N-soliton solutions are obtained via the bilinear method, and some important physical quantities and asymptotic analysis of one-soliton and two-soliton solutions are discussed. The results obtained in this paper might be useful for understanding the propagation of high-frequency waves.

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
Journal of Nonlinear Mathematical Physics
Journal of Nonlinear Mathematical Physics PHYSICS, MATHEMATICAL-PHYSICS, MATHEMATICAL
CiteScore
1.60
自引率
0.00%
发文量
67
审稿时长
3 months
期刊介绍: Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics. The main subjects are: -Nonlinear Equations of Mathematical Physics- Quantum Algebras and Integrability- Discrete Integrable Systems and Discrete Geometry- Applications of Lie Group Theory and Lie Algebras- Non-Commutative Geometry- Super Geometry and Super Integrable System- Integrability and Nonintegrability, Painleve Analysis- Inverse Scattering Method- Geometry of Soliton Equations and Applications of Twistor Theory- Classical and Quantum Many Body Problems- Deformation and Geometric Quantization- Instanton, Monopoles and Gauge Theory- Differential Geometry and Mathematical Physics
期刊最新文献
Hierarchical Neural Networks, p-Adic PDEs, and Applications to Image Processing Cosymplectic Geometry, Reductions, and Energy-Momentum Methods with Applications Existence of Positive Solutions for Hadamard-Type Fractional Boundary Value Problems at Resonance on an Infinite Interval Radial Solutions for p-k-Hessian Equations and Systems with Gradient Term Gap Theorems for Compact Quasi Sasaki–Ricci Solitons
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1