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

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  • 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.

    Mathematics Subject Classification: Primary: 35Q53, 35B35, 76B25; Secondary: 35A15, 76B15.


    \begin{equation} \\ \end{equation}
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