{"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":null,"pages":null},"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}
引用次数: 0
Abstract
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.
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