Bounded and unbounded traveling wave solutions of the (3+1)-dimensional Jimbo-Miwa equation

Bounded and unbounded traveling wave solutions of the (3+1)-dimensional Jimbo-Miwa equation

This paper studies traveling waves of the (3+1)-dimensional Jimbo-Miwa equation comprehensively and systematically. By transforming its traveling wave system into a dynamical system in R3, we apply the bifurcation method of dynamical system to investigate its phase space geometry in detail and obtai...

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Main Authors: Yuqian Zhou, Feiting Fan, Qian Liu
Format: Article
Language:English
Published: Elsevier 2019-03-01
Series:Results in Physics
Online Access:http://www.sciencedirect.com/science/article/pii/S2211379718320564
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spelling doaj-c87b77fc30a14e9784e0823860277f4c2020-11-24T22:19:29ZengElsevierResults in Physics2211-37972019-03-011211491157Bounded and unbounded traveling wave solutions of the (3+1)-dimensional Jimbo-Miwa equationYuqian Zhou0Feiting Fan1Qian Liu2College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan 610225, PR ChinaCollege of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan 610225, PR ChinaSchool of Computer Science and Technology, Southwest Minzu University, Chengdu, Sichuan 610041, PR China; Corresponding author.This paper studies traveling waves of the (3+1)-dimensional Jimbo-Miwa equation comprehensively and systematically. By transforming its traveling wave system into a dynamical system in R3, we apply the bifurcation method of dynamical system to investigate its phase space geometry in detail and obtain the parameter bifurcation sets in which various types of bounded and unbounded traveling waves are identified and simulated. Furthermore, by calculating the complicated elliptic integrals, without any loss, we give exact expressions of all traveling wave solutions of the (3+1)-dimensional Jimbo-Miwa equation, including the bounded and unbounded ones. Keywords: Jimbo-Miwa equation, Traveling waves, Dynamical system, Bifurcation, Elliptic integralhttp://www.sciencedirect.com/science/article/pii/S2211379718320564
collection DOAJ
language English
format Article
sources DOAJ
author Yuqian Zhou
Feiting Fan
Qian Liu
spellingShingle Yuqian Zhou
Feiting Fan
Qian Liu
Bounded and unbounded traveling wave solutions of the (3+1)-dimensional Jimbo-Miwa equation
Results in Physics
author_facet Yuqian Zhou
Feiting Fan
Qian Liu
author_sort Yuqian Zhou
title Bounded and unbounded traveling wave solutions of the (3+1)-dimensional Jimbo-Miwa equation
title_short Bounded and unbounded traveling wave solutions of the (3+1)-dimensional Jimbo-Miwa equation
title_full Bounded and unbounded traveling wave solutions of the (3+1)-dimensional Jimbo-Miwa equation
title_fullStr Bounded and unbounded traveling wave solutions of the (3+1)-dimensional Jimbo-Miwa equation
title_full_unstemmed Bounded and unbounded traveling wave solutions of the (3+1)-dimensional Jimbo-Miwa equation
title_sort bounded and unbounded traveling wave solutions of the (3+1)-dimensional jimbo-miwa equation
publisher Elsevier
series Results in Physics
issn 2211-3797
publishDate 2019-03-01
description This paper studies traveling waves of the (3+1)-dimensional Jimbo-Miwa equation comprehensively and systematically. By transforming its traveling wave system into a dynamical system in R3, we apply the bifurcation method of dynamical system to investigate its phase space geometry in detail and obtain the parameter bifurcation sets in which various types of bounded and unbounded traveling waves are identified and simulated. Furthermore, by calculating the complicated elliptic integrals, without any loss, we give exact expressions of all traveling wave solutions of the (3+1)-dimensional Jimbo-Miwa equation, including the bounded and unbounded ones. Keywords: Jimbo-Miwa equation, Traveling waves, Dynamical system, Bifurcation, Elliptic integral
url http://www.sciencedirect.com/science/article/pii/S2211379718320564
work_keys_str_mv AT yuqianzhou boundedandunboundedtravelingwavesolutionsofthe31dimensionaljimbomiwaequation
AT feitingfan boundedandunboundedtravelingwavesolutionsofthe31dimensionaljimbomiwaequation
AT qianliu boundedandunboundedtravelingwavesolutionsofthe31dimensionaljimbomiwaequation
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