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A New Integrable Equation with Peakon Solutions |
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| Authors: | A Degasperis D D Holm A N W Hone |
| Institution: | (1) Dipartimento di Fisica, Universitá degli Studi di Roma  La Sapienza, , Rome, Italy;(2) Sezione di Roma, Istituto Nazionale di Fisica Nucleare, Rome, Italy;(3) Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, N. Mex., USA;(4) Institute of Mathematics and Statistics, University of Kent, Canterbury, UK |
| Abstract: | 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. |
| Keywords: | peakons reciprocal transformations weak solutions |
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