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Euler-Poincaré Formalism of (Two Component) Degasperis-Procesi and Holm-Staley type Systems
Partha GuhaAbstract
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 differential equations, known as
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
- Received:
- 13.09.07
- Published:
- 13.09.07
- MSC Codes:
- 37K65, 37K10, 58D05
- Keywords:
- Virasoro algebra, Sobolev metric, Euler-Poincare