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Nearly-Hamiltonian Structure for Water Waves with Constant Vorticity
Adrian Constantin, Rossen I. Ivanov, Emil M. Prodanov
We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for ste…
Inverse Scattering Transform for the Camassa-Holm equation
Adrian Constantin, Vladimir S. Gerdjikov, Rossen I. Ivanov
An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are explici…
Poisson structure and Action-Angle variables for the Camassa-Holm equation
Adrian Constantin, Rossen I. Ivanov
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.