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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