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A nonlinear generalization of the Camassa-Holm equation with peakon solutions

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  • A nonlinearly generalized Camassa-Holm equation, depending an arbitrary nonlinearity power $p \neq 0$, 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 $p \neq 0$.
    Mathematics Subject Classification: Primary: 34C14, 37J15; Secondary: 70S10.


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