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Bifurcations of Travelling Wave Solutions for a Two-Component Camassa-Holm Equation 被引量：6

Bifurcations of Travelling Wave Solutions for a Two-Component Camassa-Holm Equation
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摘要 By using the method of dynamical systems to the two-component generalization of the Camassa-Holm equation, the existence of solitary wave solutions, kink and anti-kink wave solutions, and uncountably infinite many breaking wave solutions, smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of travelling wave solutions are listed. By using the method of dynamical systems to the two-component generalization of the Camassa-Holm equation, the existence of solitary wave solutions, kink and anti-kink wave solutions, and uncountably infinite many breaking wave solutions, smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of travelling wave solutions are listed.
作者 Ji Bin LI Yi Shen LI
机构地区 Center for Nonlinear Science Studies Department of Mathematics Department of Mathematics and Center of Nonlinear Science
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2008年第8期1319-1330,共12页 数学学报（英文版）
基金 the National Natural Science Foundation of China (10671179) and (10772158)
关键词 solitary wave kink wave solution periodic wave solution breaking wave solution smooth- ness of wave solitary wave, kink wave solution, periodic wave solution, breaking wave solution, smooth- ness of wave
分类号 O192 [理学—基础数学] O175.1 [理学—基础数学]
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参考文献8

  • 1Chen, M., Liu, S. Q., Zhang, Y. J.: A 2-component generalization of the Cammassa-Holm equation and its solution. Letters in Math. Phys., 75, 1-15 (2006)
  • 2Cammasa, R., Holm, D. D.: An integrable shallow water equation with peaked solution. Phys. Rev. Lett., 71, 1161-1164 (1993)
  • 3Cammasa, R., Holml D. D., Hyman, J. M.: A new integrable shallow water equation. Adv. Appl. Mech., 31, 1-33 (1994)
  • 4Li, J. B., Dai, H. H.: On the Study of Singular Nonlinear Travelling Wave Equations, Dynamical Approach, Science Press, Beijing, 2007
  • 5Li, J. B., Wul J. H.,Zhu, H. P.: Travelling waves for an integrable higher order kdV type wave equations. International Journal of Bifurcation and Chaos, 16(8), 2235-2260 (2006)
  • 6Li, J. B., Chen, G. R.: On a class of singular nonlinear traveling wave equations. International Journal of Bifurcation and Chaos, 17(11), (2007)
  • 7Perko, L.: Differential Equations and Dynamical Systems, Springer-Verlag, New York, 1991
  • 8Byrd, P. F., Fridman, M. D.: Handbook of Elliptic Integrals for Engineers and Sciensists, Springer, Berlin, 1971

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Acta Mathematica Sinica,English Series
2008年 第8期

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