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Integrable and non-integrable equations with peakons

A. Degasperis·D. D. Holm·A. N. W. Hone
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Abstract

We consider a one-parameter family of non-evolutionary partial differential equations which includes the integrable Camassa-Holm equation and a new equation first isolated by Degasperis and Procesi. A Lagrangian and Hamiltonian formulation is presented for the whole family of equations, and we discuss how this fits into a bi-Hamiltonian framework in the integrable cases. The Hamiltonian dynamics of peakons and some other special finite-dimensional reductions are also described.

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A. Degasperis, D. D. Holm, A. N. W. Hone. 2002-09-03. Integrable and non-integrable equations with peakons. https://doi.org/10.1142/9789812704467_0005

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