Poisson structure and Action-Angle variables for the Camassa-Holm equation

Abstract

The Poisson brackets for the scattering data of the Camassa-Holm equation are computed. Consequently, the action-angle variables are expressed in terms of the scattering data.

20 pages, LaTeX. The original publication is available at www.springerlink.com

References in corpus (4)

• An integrable shallow water equation with peaked solitons
• Multipeakons and a theorem of Stieltjes
• The Camassa-Holm Equation: Conserved Quantities and the Initial Value Problem
• Canonically conjugate variables for the periodic Camassa-Holm equation

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• Smooth and Peaked Solitons of the CH equation
• On integrability of the Camassa-Holm equation and its invariants. A geometrical approach
• On the absolutely continuous spectrum of generalized indefinite strings
• The Camassa--Holm Equation and The String Density Problem
• Equations of the Camassa-Holm Hierarchy
• Generalised Fourier Transform and Perturbations to Soliton Equations
• On the absolutely continuous spectrum of generalized indefinite strings II
• Long-time asymptotic solution structure of Camassa-Holm equation subject to an initial condition with non-zero reflection coefficient of the scattering data
• Conformal and geometric properties of the Camassa-Holm hierarchy
• Algebraic Discretization of the Camassa-Holm and Hunter-Saxton Equations