STABILITY OF SOLITARY-WAVE SOLUTIONS TO THE HIROTA-SATSUMA EQUATION

被引：0
|
作者：
Bona, Jerry L. [1 ]
Pilod, Didier [2 ]
机构：
[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA
[2] Univ Fed Rio de Janeiro, Inst Math, UFRJ, BR-21945970 Rio De Janeiro, Brazil
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 27卷 / 04期
关键词：
Solitary waves; stability; nonlinear dispersive wave equations; Korteweg-de Vries-type equations; MODEL-EQUATIONS;
D O I：
10.3934/dcds.2010.27.1391
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The evolution equation u(t) - u(xxt) + u(x) - uu(t) + ux integral(+infinity)(x) u(t)dx' = 0, (1) was developed by Hirota and Satsuma as an approximate model for unidirectional propagation of long-crested water waves. It possesses solitary-wave solutions just as do the related Korteweg-de Vries and Benjamin-Bona-Mahony equations. Using the recently developed theory for the initial-value problem for (1) and an analysis of an associated Liapunov functional, nonlinear stability of these solitary waves is established.
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页码：1391 / 1413
页数：23
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