A Note on Traveling Wave Solutions to the Two Component Camassa—Holm Equation

被引：0
作者：
Keivan Mohajer
机构：
[1] University of Saskatchewan,Department of Mathematics and Statistics
来源：
Journal of Nonlinear Mathematical Physics | 2009年 / 16卷
关键词：
Camassa—Holm equation; traveling waves; peakons; 35Q35; 35Q53;
D O I：
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学科分类号：
摘要：
In this paper we show that non-smooth functions which are distributional traveling wave solutions to the two component Camassa—Holm equation are distributional traveling wave solutions to the Camassa–Holm equation provided that the set u−1(c), where c is the speed of the wave, is of measure zero. In particular there are no new peakon or cuspon solutions beyond those already satisfying the Camassa–Holm equation. However, the two component Camassa—Holm equation has distinct from Camassa—Holm equation smooth traveling wave solutions as well as new distributional solutions when the measure of u−1(c) is not zero. We provide examples of such solutions.
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页码：117 / 125
页数：8
相关论文
共 25 条
[1]  
Camassa R(1993)An integrable shallow water equation with peaked solitons, Phys Rev. Lett 71 1661-1664
[2]  
Holm D D(2006)A two-component generalization of the Camassa–Holm equation and its solutions, Lett Math. Phys 75 1-15
[3]  
Chen M(2006)The trajectories of particles in Stokes waves, Invent Math 166 523-535
[4]  
Liu S(2007)Particle trajectories in solitary water waves Bull. Amer. Math. Soc 44 423-431
[5]  
Zhang Y(2000)Stability of peakons, Comm. Pure Appl Math 53 603-610
[6]  
Constantin A(2001)Orbital stability of solitary waves for a shallow water equation Physica D 157 75-89
[7]  
Constantin A(1999)A shallow water equation on the circle, Comm. Pure Appl Math 52 949-982
[8]  
Escher J(2001)On the scattering problem for the Camassa–Holm equation Proc. Roy. Soc. Lond 457 953-970
[9]  
Constantin A(2006)Inverse scattering transform for the Camassa–Holm equation Inverse Problems 22 2197-2207
[10]  
Strauss W A(2007)Well-posedness and blow-up phenomena for the 2-component Camassa–Holm equation, Discrete Contin. Dyn Syst 19 493-513
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