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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 |
$ 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.
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