华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (5): 67-72, .

• 应用数学与基础数学 • 上一篇    下一篇

DGH方程的尖峰孤立子的稳定性

陈会萍   

  1. 南通大学 杏林学院, 江苏 南通 226007
  • 收稿日期:2009-10-01 修回日期:2010-02-01 出版日期:2010-09-25 发布日期:2010-09-25
  • 通讯作者: 陈会萍

Stability of peakons for the DGH equation

CHEN Hui-ping   

  1. Xinglin School, Nantong University, Nantong Jiangsu 226007, China
  • Received:2009-10-01 Revised:2010-02-01 Online:2010-09-25 Published:2010-09-25
  • Contact: CHEN Hui-ping

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摘要： 尖峰孤立子是一个非线性色散方程的尖峰孤立波解, 是浅水波理论中的一个模型. 本文通过构造一个泛函和守恒律来证明DGH方程的尖峰孤立子在H^1中的轨道稳定性. 该稳定性定理表明, 如果一个波在开始时与尖锋孤立子接近,则在之后的任何时间仍然与它接近.

关键词: 稳定性, DGH方程, 孤立子, 稳定性, DGH方程, 孤立子

Abstract: The peakons are peaked solitary wave solutions of a certain nolinear dispersive equation that is a model in shallow water theory. In this paper, the author showed that the peaked solitons to the DGH equation were orbital stable in H^1 norm by constructing a functional and conservation laws. The stability theorem indicates that, if a wave is close to the peakons at the beginning, it will remain close to some translate of it at any time later.

Key words: the DGH equation, peakons, stability, the DGH equation, peakons

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