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On Integrability of the Camassa–Holm Equation and Its Invariants

A Geometrical Approch

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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).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Physics, Lomonosov MSU, Vorob’evy Hills, Moscow, 119902, Russia

    V. Golovko

  2. University of Twente, Postbus 217, 7500 AE, Enschede, the Netherlands

    P. Kersten

  3. Independent University of Moscow, B. Vlasevsky 11, 119002, Moscow, Russia

    I. Krasil’shchik & A. Verbovetsky

Authors
  1. V. Golovko
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  2. P. Kersten
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  3. I. Krasil’shchik
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  4. A. Verbovetsky
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Corresponding author

Correspondence to I. Krasil’shchik.

Additional information

This work was supported in part by the NWO–RFBR grant 047.017.015 and RFBR–Consortium E.I.N.S.T.E.I.N. grant 06-01-92060.

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Golovko, V., Kersten, P., Krasil’shchik, I. et al. On Integrability of the Camassa–Holm Equation and Its Invariants. Acta Appl Math 101, 59–83 (2008). https://doi.org/10.1007/s10440-008-9200-z

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  • DOI: https://doi.org/10.1007/s10440-008-9200-z

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