  We consider a generalization of the Camassa Holm (CH) equation with two
dependent variables, called CH2, introduced by Liu and Zhang. We briefly
provide an alternative derivation of it based on the theory of Hamiltonian
structures on (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
provide 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.
