# American Institute of Mathematical Sciences

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 and Continuous Dynamical Systems, 2010, 27 (4) : 1391-1413. doi: 10.3934/dcds.2010.27.1391
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