Euler-Poincaré Formalism of (Two Component) Degasperis-Procesi and Holm-Staley type Systems

DOI

10.2991/jnmp.2007.14.3.8How to use a DOI?

Abstract

In this paper we propose an Euler-Poincaré formalism of the Degasperis and Procesi (DP) equation. This is a second member of a one-parameter family of partial dif- ferential equations, known as b-field equations. This one-parameter family of pdes includes the integrable Camassa-Holm equation as a first member. We show that our Euler-Poincaré formalism exactly coincides with the Degasperis-Holm-Hone (DHH) Hamiltonian framework. We obtain the DHH Hamiltonian structues of the DP equa- tion from our method. Recently this new equation has been generalized by Holm and Staley by adding viscosity term. We also discuss Euler-Poincaré formalism of the Holm-Staley equation. In the second half of the paper we consider a generalization of the Degasperis and Procesi (DP) equation with two dependent variables. we study the Euler-Poincaré framework of the 2–component Degasperis-Procesi equation. We also mention the b-family equation.

Copyright

© 2007, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Partha Guha
PY  - 2007
DA  - 2007/10/01
TI  - Euler-Poincaré Formalism of (Two Component) Degasperis-Procesi and Holm-Staley type Systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 398
EP  - 429
VL  - 14
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2007.14.3.8
DO  - 10.2991/jnmp.2007.14.3.8
ID  - Guha2007
ER  -