{"title":"EXACT TRAVELLING WAVE SOLUTIONS FOR THE GENERALIZED KURAMOTO-SIVASHINSKY EQUATION","authors":"Jian Yang, Xiaojuan Lu, Shengqiang Tang","doi":"10.18642/jmsaa_7100121422","DOIUrl":null,"url":null,"abstract":"By using transformation , 2 3 2 1 u a u a a u + + = ′ ′ the method of sine-cosine and the method of dynamical bifurcation theory of the differentiable dynamics, we study the generalized Kuramoto-Sivashinsky equation. It is shown that the generalized Kuramoto-Sivashinsky equation gives solitary wave solution, solitary patterns wave solution, and periodic wave solution. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. All exact explicit parametric representations of the above waves are determined.","PeriodicalId":49916,"journal":{"name":"Latin American Applied Research","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"15","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Latin American Applied Research","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.18642/jmsaa_7100121422","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, CHEMICAL","Score":null,"Total":0}
引用次数: 15
Abstract
By using transformation , 2 3 2 1 u a u a a u + + = ′ ′ the method of sine-cosine and the method of dynamical bifurcation theory of the differentiable dynamics, we study the generalized Kuramoto-Sivashinsky equation. It is shown that the generalized Kuramoto-Sivashinsky equation gives solitary wave solution, solitary patterns wave solution, and periodic wave solution. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. All exact explicit parametric representations of the above waves are determined.
利用变换、2 3 2 1 ua ua a u + + = ' '、正弦-余弦方法和可微动力学的动力分岔理论方法，研究了广义Kuramoto-Sivashinsky方程。证明了广义Kuramoto-Sivashinsky方程给出了孤波解、孤型波解和周期波解。在不同的参数条件下，给出了保证上述解存在的各种充分条件。确定了上述波的所有精确的显式参数表示。
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