He's Semi-inverse Method for Camassa-Holm Equation and Simplied Modied Camassa-Holm Equation

Decomposition Method for Camassa-holm Equation

On the Camassa-Holm equation

This talk is focused on recent progress of studies for the Camassa-Holm equation. First, we will give a brief review on the derivations, well-posedness for the strong solution, blow-up phenomenon and existence of the weak solutions. Then, infinite propagation speed for the Camassa-Holm equation will be proved in the following sense: the corresponding solution u(x, t) with compactly supported in...

Attractors for the Viscous Camassa-holm Equation

Abstract. We consider the viscous Camassa-Holm equation subject to an external force, where the viscosity term is given by second order differential operator in divergence form. We show that under some mild assumptions on the viscosity term, one has global wellposedness both in the periodic case and the case of the whole line. In the periodic case, we show the existence of global attractors in ...

Inverse Scattering Transform for the Camassa-Holm equation

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 constructed in terms of the scattering data. The main difference with respect to the standard Inverse Scattering Transform lies in the fact that we have a weighted spectral problem. We therefore have to develop different asy...

Dissipative Solutions for the Camassa–holm Equation

has been extensively studied since the first systematic analysis in [5, 6]. Part of the attraction is the surprising complexity of the equation and its deep and nontrivial properties. To list a few of its peculiarities: The Camassa–Holm equation has a bi-Hamiltonian structure [16], it is completely integrable [5], and it has infinitely many conserved quantities [5]. Here we study the equation w...