Solitons in the Camassa-Holm Shallow Water Equation

preprint1993arXivOpen access

Abstract

We study the class of shallow water equations of Camassa and Holm derived from the Lagrangian: L=∫(12(φxxx−φx)φt−12(φx)3−12φx(φxx)2−12κφx2)dx, L= \int \left( \frac{1}{2} (φ_{xxx}-φ_{x} )φ_{t} - {1 \over 2} {(φ_{x})^{3}} - {1 \over 2}φ_{x}(φ_{xx})^{2} - {1 \over 2} κφ_{x}^{2} \right) dx,

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