Stability of Solitary-Wave Solutions of Systems of Dispersive Equations

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• 作者：Jerry L. Bona ; Hongqiu Chen ; Ohannes Karakashian
• 刊名：Applied Mathematics & Optimization
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：75
• 期：1
• 页码：27-53
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Phy
• 出版者：Springer US
• ISSN：1432-0606
• 卷排序：75

文摘

The present study is concerned with systems $$\begin{aligned} \left\{ \begin{array}{ll} &{} \frac{\partial u}{\partial t} +\frac{\partial ^3 u}{\partial x^3} + \frac{\partial }{\partial x}P(u, v)=0,\\ &{} \frac{\partial v}{\partial t} +\frac{\partial ^3 v}{\partial x^3} + \frac{\partial }{\partial x}Q(u, v)=0, \end{array}\right. \end{aligned}$$of Korteweg–de Vries type, coupled through their nonlinear terms. Here, \(u = u(x,t)\) and \(v = v(x,t)\) are real-valued functions of a real spatial variable x and a real temporal variable t. The nonlinearities P and Q are homogeneous, quadratic polynomials with real coefficients \(A,B,\ldots \), viz.$$\begin{aligned} P(u,v)=Au^2+Buv+Cv^2, \qquad Q(u,v)=Du^2+Euv+Fv^2, \end{aligned}$$in the dependent variables u and v. A satisfactory theory of local well-posedness is in place for such systems. Here, attention is drawn to their solitary-wave solutions. Special traveling waves termed proportional solitary waves are introduced and determined. 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PDE 12, 1133–1173 (1987)MathSciNetCrossRefMATHGoogle ScholarCopyright information© Springer Science+Business Media New York 2015Authors and AffiliationsJerry L. Bona1Email authorHongqiu Chen2Ohannes Karakashian31.The Department of Mathematics, Statistics and Computer ScienceThe University of Illinois at ChicagoChicagoUSA2.Department of Mathematical SciencesThe University of MemphisMemphisUSA3.Department of MathematicsThe University of TennesseeKnoxvilleUSA About this article CrossMark Publisher Name Springer US Print ISSN 0095-4616 Online ISSN 1432-0606 About this journal Reprints and Permissions Article actions .buybox { margin: 16px 0 0; position: relative; } .buybox { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; font-size: 14px; font-size: .875rem; } .buybox { zoom: 1; } .buybox:after, .buybox:before { content: ''; display: table; } .buybox:after { clear: both; } /*---------------------------------*/ .buybox .buybox__header { border: 1px solid #b3b3b3; border-bottom: 0; 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