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We consider a generalization of the Camassa Holm (CH) equation with twodependent variables, called CH2, introduced by Liu and Zhang. We brieflyprovide an alternative derivation of it based on the theory of Hamiltonianstructures on (the dual of) a Lie Algebra. The Lie Algebra here involved is thesame algebra underlying the NLS hierarchy. We study the structural propertiesof the CH2 hierarchy within the bihamiltonian theory of integrable PDEs, andprovide its Lax representation. Then we explicitly discuss how to constructclasses of solutions, both of peakon and of algebro-geometrical type. Wefinally sketch the construction of a class of singular solutions, defined bysetting to zero one of the two dependent variables.Comment: 22 pages, 2 figures. A few typos correcte

On a Camassa–Holm type equation with two dependent variables