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K(n,-n,2n)方程的行波解 被引量：1

Traveling wave solutions of equation K(n,-n,2n)
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摘要 利用动力系统分支理论和定性理论研究了K(n,-n,2n)方程的行波解及其动力学性质.结合可积系统的特点,得到系统的孤立行波解,不可数无穷多光滑周期行波解和不光滑行波解;并根据行波解与相轨线间关系,揭示了不同类型行波解间转变与参数变化的关系. The traveling wave solutions and the dynamical properties of Equation K（n,-n, 2n） were studied in terms of the bifurcation theory of dynamic systems and of the qualitative theory. Based on the characters of an integrable system, the solitary traveling wave solutions, uncountably infinite many smooth periodic wave solutions and non-smooth periodic traveling wave solutions of the system were obtained. According to the relationship between traveling waves and phase orbits, that changes of parameters led to the transitions of traveling wave solutions of different types were revealed.
作者 毕平 仇钊成
机构地区 华东师范大学数学系
出处 《华东师范大学学报（自然科学版）》 CAS CSCD 北大核心 2009年第1期68-77,共10页 Journal of East China Normal University(Natural Science)
基金 国家自然科学基金(10671069) 上海市重点学科建设项目(B407) 上海市自然科学基金(08ZR1407000)
关键词 行波解 孤立波 周期波 尖波 光滑波 traveling wave solitary wave periodic wave cusp wave smooth wave
分类号 O175.25 [理学—基础数学]
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参考文献8

  • 1KADOMTSEV B B, PETVIASHVILI V I. On the stability of solitary waves in weakly dispersive media[J]. Soy Phys Dokl, 1970(5): 539-541.
  • 2ZAKHAROV V E, KUZNETSOV E A. On the three-dimensional solitons[J]. Soy Phys, 1974, 39: 285-288.
  • 3WAZWAZ A M. Compact structures for variants of the generalizes Kdv and the generalized Kp equations[J]. Applied Mathematics and Computation, 2004, 149: 103-117.
  • 4WAZWAZ A M. Compactons and solitary patterns structures for variants of the Kdv and the Kp equtions[J]. Appl Math Comput, 2003, 139(1): 37-54.
  • 5WAZWAZ A M. An analytic study of compactons structures in a class of nonlinear dispersive equations[J]. Math Comput Simul, 2003, 63(1): 35-44.
  • 6WAZWAZ A M. Explicit travelling wave solutions of variants of the K(n,n) and the ZK(n,n) equtions with compact andnoncompact structuers[J]. Applied Mathematics and Compution, 2006, 173: 213-230.
  • 7LI J B, DAI H H. On the Study of Singular Nonlinear Traveling Wave Equation: Dynamical System Approach[M]. Beijing: Science Press, 2007.
  • 8TANG S Q, LI M. Bifurcations of traveling wave solutions in a class of generalized Kdv equation[J]. Applied Mathematics and Computation, 2006, 177: 589-596.

同被引文献11

  • 1Kadomtsev B B, Petviashvili V I. On the stability of solitary waves in weakly dispersive media[J]. Sov Phys, 1970, 15: 539-541.
  • 2Zakharov V E, Kuznetsov E A. On the three-dimensional solitons[J]. Sov Phys, 1974, 39: 285-288.
  • 3Wazwaz A M. Compact structures for variants of the generalized KdV and the generalized KP equations[J]. Appl Math Comput, 2004, 149: 103-117.
  • 4Wazwaz A M. Compactons and solitary patterns structures for variants of the KdV and the KP equations[J]. Appl Math Comput, 2003, 139(1): 37-54.
  • 5Wazwaz A M An analytic study of Compactons structures in a class of nonlinear dispersive equations[J]. Math Comput Simulation, 2003, 63(1): 35-44.
  • 6Wazwaz A M. Explicit travelling wave solutions of variants of the K(n, n) and the ZK(n, n) equations with compact and noncompact structuers[J]. Appl Math Comput, 2006, 173: 213- 230.
  • 7Li Jibin, Dai Huihui. On the Study of Singular Nonlinear Traveling Wave Equation: Dynamical System Approach[M]. Beijing: Science Press, 2007.
  • 8Tang Shengqiang, Li Ming. Bifurcations of travelling wave solutions in a class of generalized Kdv equation[J]. Appl Math Comput, 2006, 177: 589-596.
  • 9Dai Huihui. Exact traveling wave solutions of an integrable equation arising in hyperelastic rods[J]. Wave Motions, Ser B, 1998, 38: 367-381.
  • 10Dai Huihui, Huo Y. Solitary shock wave and other traveling waves in a general compressible hyperelastic rod[J]. Proc Roy Soc London Ser A, 456, 331-363.

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华东师范大学学报（自然科学版）
2009年 第1期

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