Vakhnenko方程的光滑周期波的波长

郭丽娜; 陈爱永; 黄文韬

doi:10.21656/1000-0887.370020

Vakhnenko方程的光滑周期波的波长

doi: 10.21656/1000-0887.370020

¹桂林电子科技大学数学与计算科学学院数学系, 广西桂林 541004;²贺州学院理学院数学系, 广西贺州 542800

基金项目: 国家自然科学基金(11361017)；广西自然科学基金(2015GXNSFGA139004)

详细信息

作者简介:
郭丽娜（1989—），女，硕士生(E-mail: gdzhaosf@163.com);陈爱永(1977—)，男，教授，博士，硕士生导师(通讯作者. E-mail: aiyongchen@163.com).

中图分类号: O357.41
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出版历程
- 收稿日期: 2016-01-13
- 修回日期: 2016-01-25
- 刊出日期: 2016-07-15

Wave Lengths of Periodic Waves for the Vakhnenko Equation

¹School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, P.R.China;²Department of Mathematics, College of Science,Hezhou University, Hezhou, Guangxi 542800, P.R.China

Funds: The National Natural Science Foundation of China(11361017)

摘要

摘要: 主要研究Vakhnenko方程的光滑周期行波解的波长.通过变量变换, Vakhnenko方程可以转化为一个平面多项式微分系统.利用动力系统的临界周期分支方法研究这个多项式微分系统,其主要结果是给出了周期函数T(h)或波长函数λ(a)的单调性质.与KdV方程比较, 波长函数λ(a)单调递减到一个有限的数,而不是单调递增到无穷.结果表明, 对于固定波速c, Vakhnenko方程不存在任意小或任意大波长的光滑周期行波解.
- Vakhnenko方程 /
- 周期波 /
- 周期函数 /
- 波长 /
- 单调性
Abstract: The wave lengths of smooth periodic traveling wave solutions to the Vakhnenko equation were studied. The Vakhnenko equation was reduced to a planar polynomial differential system through the transformation of variables. The polynomial differential system was treated with the critical period bifurcation method based on the dynamical system theory. The main results involve the monotonicity properties of periodic function T(h) (or wave length function λ(a)). In comparison with the wave length for the KdV equation, wave length function λ(a) monotonically decreases to a finite value rather than monotonically increases to infinity. This shows that, for fixed wave speed c, there exist no smooth periodic wave solutions with arbitrarily small wave lengths or arbitrarily large wave lengths, to the Vakhnenko equation.
- Vakhnenko equation /
- periodic wave /
- periodic function /
- wave length /
- monotonicity

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参考文献(20)

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