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Peaked wave solutions of CH-r equation 被引量：2

Peaked wave solutions of CH-r equation
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摘要 In this paper the qualitative analysis methods of planar autonomous systems and numerical simu-lation are used to investigate the peaked wave solutions of CH-r equation. Some explicit expressions of peakedsolitary wave solutions and peaked periodic wave solutions are obtained, and some of their relationships arerevealed. Why peaked points are generated is discussed. In this paper the qualitative analysis methods of planar autonomous systems and numerical simulation are used to investigate the peaked wave solutions of CH-r equation. Some explicit expressions of peaked solitary wave solutions and peaked periodic wave solutions are obtained, and some of their relationships are revealed. Why peaked points are generated is discussed.
作者 郭柏灵 刘正荣
机构地区 Institute of Applied Physics and Computational Mathematics. Beijing Department of Mathematics
出处 《Science China Mathematics》 SCIE 2003年第5期696-709,共14页 中国科学：数学（英文版）
基金 This work was supported by the National Natural Science Foundation of China(Grant No.10261008) the Natural Science Foundation of Yunnan Province(Grant No,2002A0002M).
关键词 CH-r equation peaked WAVE solutions BIFURCATION of PHASE portraits. CH-r equation peaked wave solutions bifurcation of phase portraits
分类号 O241 [理学—计算数学]
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参考文献10

  • 1Enrique G. Reyes.Geometric Integrability of the Camassa–Holm Equation[J].Letters in Mathematical Physics.2002(2)
  • 2Ciprian Foias,Darryl D. Holm,Edriss S. Titi.The Three Dimensional Viscous Camassa–Holm Equations, and Their Relation to the Navier–Stokes Equations and Turbulence Theory[J].Journal of Dynamics and Differential Equations.2002(1)
  • 3Mark S. Alber,Roberto Camassa,Yuri N. Fedorov,Darryl D. Holm,Jerrold E. Marsden.The Complex Geometry of Weak Piecewise Smooth Solutions of Integrable Nonlinear PDE’s?of Shallow Water and Dym Type[J].Communications in Mathematical Physics.2001(1)
  • 4Fuchssteiner,B.Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation, Phys[].D.1996
  • 5Constantin,A.Quasi-periodicity with respect to time of spatially periodic finite-gap solution of the Camassa-Holm equation, Bull[].Sci Math.1998
  • 6Kouranbaeva,S.The Camassa-Holm equation as a geodesic flow on the diffeomorphism group, J[].Journal of Mathematical Physics.1999
  • 7Boyd,J. P.Peakons and coshoidal waves: travelling wave solutions of the Camassa-Holm equation, Appl[].Mathematics of Computation.1997
  • 8Constantin,A.On the Cauchy problem for the periodic Camassa-Holm equation, J[].Differential Equations.1997
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同被引文献4

引证文献2

  • 1CHEN ChunLi~(1+) LI YiShen~2 ZHANG JinE~3 1 Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China,2 Department of Mathematics,University of Science and Technology of China,Hefei 230026,China,3 SB and SEF,University of Hong Kong,Pokfulam Road,Hong Kong,China.The multi-soliton solutions of the CH-γ equation[J].Science China Mathematics,2008,51(2):314-320. 被引量：3
  • 2DENG ShengFu1, GUO BoLing2 & WANG TingChun2,3 1Department of Mathematics, Zhanjiang Normal University, Zhanjiang 524048, China,2Institute of Applied Physics and Computational Mathematics, Beijing 100088, China,3 College of Math and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China.Travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation[J].Science China Mathematics,2011,54(3):555-572. 被引量：5

二级引证文献8

Science China Mathematics
2003年 第5期

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