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Vakhnenko方程的光滑周期波的波长

郭丽娜 陈爱永 黄文韬

郭丽娜, 陈爱永, 黄文韬. Vakhnenko方程的光滑周期波的波长[J]. 应用数学和力学, 2016, 37(7): 678-690. doi: 10.21656/1000-0887.370020
引用本文: 郭丽娜, 陈爱永, 黄文韬. Vakhnenko方程的光滑周期波的波长[J]. 应用数学和力学, 2016, 37(7): 678-690. doi: 10.21656/1000-0887.370020
GUO Li-na, CHEN Ai-yong, HUANG Wen-tao. Wave Lengths of Periodic Waves for the Vakhnenko Equation[J]. Applied Mathematics and Mechanics, 2016, 37(7): 678-690. doi: 10.21656/1000-0887.370020
Citation: GUO Li-na, CHEN Ai-yong, HUANG Wen-tao. Wave Lengths of Periodic Waves for the Vakhnenko Equation[J]. Applied Mathematics and Mechanics, 2016, 37(7): 678-690. doi: 10.21656/1000-0887.370020

Vakhnenko方程的光滑周期波的波长

doi: 10.21656/1000-0887.370020
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

Wave Lengths of Periodic Waves for the Vakhnenko Equation

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

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