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K(n,-n,2n)方程的显式行波解及其动力学性质 被引量：3

Explicit traveling wave solutions of K(n,-n,2n)equation and it's dynamical behavior
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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)方程的显式行波解.并借助于行波解动力学性质对这些解进行取舍,指出一些精确的显式解可能会给出一些错误的信息,即在求解精确的显式行波解前理解该行波解的动力学行为的必要性.文章最后通过数值模拟验证了相关的结论. Some explicit traveling wave solutions of equation K（n, -n, 2n） are focused on with the help of qualitative theory and bifurcation theory of dynamical system. The dynamical behavior of traveling wave solutions helps to decide whether to choose the solutions or not, thus, some wrong information is possible to be given by precise explicit traveling wave solutions. That is, it is necessary to understand the dynamical behavior of the traveling wave solutions before finding the precise explicit traveling solutions. At last, the related conclusions are testified by means of numerical simulations.
作者 仇钊成 毕平
机构地区 南京第 华东师范大学数学系
出处 《高校应用数学学报（A辑）》 CSCD 北大核心 2009年第3期311-318,共8页 Applied Mathematics A Journal of Chinese Universities(Ser.A)
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 分支理论 traveling wave solution solitary wave periodic wave cusp wave smooth wave bifurcation theory
分类号 O175.25 [理学—基础数学]
  • 相关文献

参考文献12

  • 1Kadomtsev B B, Petviashvili V I. On the stability of solitary waves in weakly dispersive media[J]. Sov Phys, 1970, 15: 539-541.
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  • 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.
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二级参考文献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9

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二级引证文献2

高校应用数学学报（A辑）
2009年 第3期

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