TY - RPRT T1 - On a Camassa-Holm type equation with two dependent variables Y1 - 2006 A1 - Gregorio Falqui AB - We consider a generalization of the Camassa Holm (CH) equation with two dependent variables, called CH2, introduced in [16]. We briefly provide an alternative derivation of it based on the theory of Hamiltonian structures\\non (the dual of) a Lie Algebra. The Lie Algebra here involved is the same algebra underlying the NLS hierarchy. We study the structural properties of the CH2 hierarchy within the bihamiltonian theory of integrable PDEs, and\\nprovide its Lax representation. Then we explicitly discuss how to construct classes of solutions, both of peakon and of algebro-geometrical type. We finally sketch the construction of a class of singular solutions, defined by setting to zero one of the two dependent variables. JF - J. Phys. A 39 (2006) 327-342 UR - http://hdl.handle.net/1963/1721 U1 - 2430 U2 - Mathematics U3 - Mathematical Physics ER -