# A camassa—Holm equation interacted with the degasperis—procesi equation

Research paper by Ziemowit Popowicz

Indexed on: 01 Oct '06Published on: 01 Oct '06Published in: Czechoslovak Journal of Physics

#### Abstract

We present two different Hamiltonian extensions of the Degasperis-Procesi equation. The construction based on the observation that the second Hamiltonian operator of the Degasperis-Procesi equation could be considered as the Dirac reduced Poisson tensor of the second Hamiltonian operator of the Boussinesq equation. The first extension describes the interaction between Camassa-Holm and Degasperis-Procesi equation while the second gives us the two component generalization of the Degasperis-Procesi equation.