On integrability of the Camassa-Holm equation and its invariants. A geometrical approach

Abstract

Using geometrical approach exposed in arXiv:math/0304245 and arXiv:nlin/0511012, we explore the Camassa-Holm equation (both in its initial scalar form, and in the form of 2x2-system). We describe Hamiltonian and symplectic structures, recursion operators and infinite series of symmetries and conservation laws (local and nonlocal).

arXiv comment24 pages

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Cited by in corpus (5)

• Geometry of jet spaces and integrable systems
• Bäcklund transformations for the Camassa-Holm equation
• A unified approach to computation of integrable structures
• On integrable structures for a generalized Monge-Ampere equation
• The Calogero--Bogoyavlenskii--Schiff breaking soliton equation: recursion operators and higher symmetries