Acta Applicandae Mathematicae

, Volume 101, Issue 1, pp 59–83

On Integrability of the Camassa–Holm Equation and Its Invariants

A Geometrical Approch
  • V. Golovko
  • P. Kersten
  • I. Krasil’shchik
  • A. Verbovetsky
Article

DOI: 10.1007/s10440-008-9200-z

Cite this article as:
Golovko, V., Kersten, P., Krasil’shchik, I. et al. Acta Appl Math (2008) 101: 59. doi:10.1007/s10440-008-9200-z

Abstract

Using geometrical approach exposed in (Kersten et al. in J. Geom. Phys. 50:273–302, [2004] and Acta Appl. Math. 90:143–178, [2005]), we explore the Camassa–Holm equation (both in its initial scalar form, and in the form of 2×2-system). We describe Hamiltonian and symplectic structures, recursion operators and infinite series of symmetries and conservation laws (local and nonlocal).

Keywords

Camassa–Holm equation Integrability Hamiltonian structures Symplectic structures Recursion operators Symmetries Conservation laws Geometrical approach 

Mathematics Subject Classification (2000)

37K05 35Q53 

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • V. Golovko
    • 1
  • P. Kersten
    • 2
  • I. Krasil’shchik
    • 3
  • A. Verbovetsky
    • 3
  1. 1.Department of Mathematics, Faculty of PhysicsLomonosov MSUMoscowRussia
  2. 2.University of TwenteEnschedethe Netherlands
  3. 3.Independent University of MoscowMoscowRussia

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