A nonlinear generalization of the Camassa-Holm equation with peakon solutions
Abstract
A nonlinearly generalized Camassa-Holm equation, depending an arbitrary nonlinearity power p ≠ 0, is considered. This equation reduces to the Camassa-Holm equation when p=1 and shares one of the Hamiltonian structures of the Camassa-Holm equation. Two main results are obtained. A classification of point symmetries is presented and a peakon solution is derived, for all powers p ≠ 0.
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