Solitons in the Camassa-Holm Shallow Water Equation

Nonlinear Sciences – Pattern Formation and Solitons

Scientific paper

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8 pages, LaTex, no figures

Scientific paper

We study the class of shallow water equations of Camassa and Holm derived
from the Lagrangian: $ L= \int \left( \frac{1}{2} (\varphi_{xxx}-\varphi_{x}
)\varphi_{t} - {1 \over 2} {(\varphi_{x})^{3}} - {1 \over
2}\varphi_{x}(\varphi_{xx})^{2} - {1 \over 2} \kappa \varphi_{x}^{2} \right)
dx, $

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