Reciprocal link for a three-component Camassa-Holm type equation

Modulation of Camassa–Holm equation and reciprocal transformations

We derive the modulation equations or Whitham equations for the Camassa– Holm (CH) equation. We show that the modulation equations are hyperbolic and admit bi-Hamiltonian structure. Furthermore they are connected by a reciprocal transformation to the modulation equations of the first negative flow of the Korteweg de Vries (KdV) equation. The reciprocal transformation is generated by the Casimir...

Singular solutions of a modified two-component Camassa-Holm equation.

The Camassa-Holm (CH) equation is a well-known integrable equation describing the velocity dynamics of shallow water waves. This equation exhibits spontaneous emergence of singular solutions (peakons) from smooth initial conditions. The CH equation has been recently extended to a two-component integrable system (CH2), which includes both velocity and density variables in the dynamics. Although ...

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...

Decomposition Method for Camassa-holm Equation

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 ...