Theoretical and Mathematical Physics

, Volume 133, Issue 2, pp 1463–1474 | Cite as

A New Integrable Equation with Peakon Solutions

  • A. Degasperis
  • D. D. Holm
  • A. N. W. Hone


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.

peakons reciprocal transformations weak solutions 


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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • A. Degasperis
    • 1
    • 2
  • D. D. Holm
    • 3
  • A. N. W. Hone
    • 4
  1. 1.Dipartimento di FisicaUniversitá degli Studi di Roma “La Sapienza,”RomeItaly
  2. 2.Sezione di Roma, Istituto Nazionale di Fisica NucleareRomeItaly
  3. 3.Theoretical Division and Center for Nonlinear StudiesLos Alamos National LaboratoryLos AlamosUSA
  4. 4.Institute of Mathematics and StatisticsUniversity of KentCanterburyUK

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