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广义Camassa-Holm方程的显式孤立子解 被引量：6

Explicit Soliton Solutions of Generalized Camassa-Holm Equation
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摘要 研究广义Camassa-Holm方程的显式孤立子解,在研究中,首先建立一个与该方程相对应的平面系统,然后画出平面系统的分支相图,最后,通过相图中某些特殊的同宿轨道获得显式孤立子解. In this paper, explicit soliton solutions of generalized Camassa-Holm equation is studied. First, a planar system corresponding to the generalized Camassa-Hohm equation is established. Secondly, the bifurcation phase portraits of the planar system are given. Finally, via some special homoclinic orbits, the explicit soliton solutions are obtained.
作者 刘正荣 杨喜艳
机构地区 华南理工大学数学科学学院
出处 《云南民族大学学报（自然科学版）》 CAS 2007年第2期89-94,共6页 Journal of Yunnan Minzu University:Natural Sciences Edition
基金 国家自然科学基金资助项目(10571062)
关键词 显式孤立子解 分支相图 广义Camassa—Holm方程 explicit soliton solutions bifurcation phase portraits generalized Camassa-Holm equation
分类号 O175.12 [理学—基础数学]
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参考文献12

  • 1LIU Z R,QIAN T F.Peakons and Their Bifurcation in a Generalized Camassa-Holm Equation[J].International Journal of Bifurcation and Choas,2001,11 (3):781-792.
  • 2CAMASSA R,HOLM D D.An Integrable Shallow Water Equation with Peaked Solitons[J].Phys Rev Lett,1993,71 (11):1661-1664.
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  • 4刘正荣.关于Camassa-Holm方程尖孤立子解的扩展(英文)[J].云南民族大学学报（自然科学版）,2004,13(1):3-9. 被引量：8
  • 5唐民刚,谢绍龙.广义CH方程的周期波解及数值模拟[J].云南民族大学学报（自然科学版）,2007,16(1):13-17. 被引量：3
  • 6LIU Z R,LONG Y.Compacton-like wave and kink-like wave of GCH Equation[J].Nonlinear Analysis:Real World Applications,2007,8(1):136-155.
  • 7YIN Z Y.On the Blow-up Scenario for the Generalized Camassa-Hohm Equation[J].Coinmunications in Partial Differential Equations,2004,29 (5/6):867-877.
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二级参考文献27

  • 1GUO Boling & LIU Zhengrong Institute of Applied Physics and Computational Mathematics, Beijing 100088, China,School of Mathematical Sciences and Center for Nonlinear Science Studies, South China University of Technology, Guangzhou 510640, China.Two new types of bounded waves of CH-γ equation[J].Science China Mathematics,2005,48(12):1618-1630. 被引量：12
  • 2ZHANG WenlingDepartment of Mathematics and Physics, National Natural Science Foundation of China, Beijing 100085, China.General expressions of peaked traveling wave solutions of CH-γ and CH equations[J].Science China Mathematics,2004,47(6):862-873. 被引量：10
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  • 10Camassa R, Holm D D. An integrable shallow water equation with peaked solitons[J]. Phys Rev Lett, 1993, 71 (11):1661 - 1664.

共引文献16

同被引文献59

引证文献6

二级引证文献5

云南民族大学学报（自然科学版）
2007年 第2期

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