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