华东师范大学学报(自然科学版) ›› 2009, Vol. 2009 ›› Issue (1): 68-77.

• 应用数学与基础数学 • 上一篇    下一篇

K(n,-n,2n)方程的行波解

毕平, 仇钊成   

  1. 华东师范大学数学系, 上海 200041
  • 收稿日期:2008-07-26 修回日期:2008-09-01 出版日期:2009-01-25 发布日期:2009-01-25
  • 通讯作者: 毕平

Traveling wave solutions of equation K(n,-n,2n) (Chinese)

BI Ping, QIU Zhao-cheng   

  1. Department of Mathematics, East China Normal University, Shanghai 200041, China
  • Received:2008-07-26 Revised:2008-09-01 Online:2009-01-25 Published:2009-01-25
  • Contact: BI Ping

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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.

关键词: 行波解, 孤立波, 周期波, 尖波, 光滑波, 行波解, 孤立波, 周期波, 尖波, 光滑波

Abstract: 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.

Key words: solitary wave, periodic wave, cusp wave, smooth wave, traveling wave, solitary wave, periodic wave, cusp wave, smooth wave

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