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).

24 pages

References in corpus (3)

• Poisson structure and Action-Angle variables for the Camassa-Holm equation
• Variational Poisson-Nijenhuis structures for partial differential equations
• (Non)local Hamiltonian and symplectic structures, recursions, and hierarchies: a new approach and applications to the N=1 supersymmetric KdV equation