alexa A New Integrable Equation with Peakon Solutions
Mathematics

Mathematics

Journal of Generalized Lie Theory and Applications

Author(s): A Degasperis, D D Holm, A N W Hone

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We consider a new partial differential equation recently obtained by Degasperis and Procesi using the method of asymptotic integrability; this equation has a form similar to the Camassa–Holm shallow water wave equation. We prove the exact integrability of the new equation by constructing its Lax pair and explain its relation to a negative flow in the Kaup–Kupershmidt hierarchy via a reciprocal transformation. The infinite sequence of conserved quantities is derived together with a proposed bi-Hamiltonian structure. The equation admits exact solutions as a superposition of multipeakons, and we describe the integrable finite-dimensional peakon dynamics and compare it with the analogous results for Camassa–Holm peakons.

This article was published in Theoretical and Mathematical Physics and referenced in Journal of Generalized Lie Theory and Applications

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