Solitons in the Camassa-Holm Shallow Water Equation

Abstract

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

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