November  2010, 27(4): 1391-1413. doi: 10.3934/dcds.2010.27.1391

Stability of solitary-wave solutions to the Hirota-Satsuma equation

1. 

Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60607, United States

2. 

UFRJ, Institute of Mathematics, Federal University of Rio de Janeiro, P.O. Box 68530, CEP: 21945-970, Rio de Janeiro, RJ, Brazil

Received  November 2009 Revised  February 2010 Published  March 2010

The evolution equation

$ u_t- $ uxxt$ +u_x-$uut$ +u_x\int_x^{+\infty}u_tdx'=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.

Citation: Jerry L. Bona, Didier Pilod. Stability of solitary-wave solutions to the Hirota-Satsuma equation. Discrete & Continuous Dynamical Systems - A, 2010, 27 (4) : 1391-1413. doi: 10.3934/dcds.2010.27.1391
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