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On a Camassa-Holm type equation with two dependent variables

TitleOn a Camassa-Holm type equation with two dependent variables
Publication TypePreprint
AuthorsFalqui, G
Series TitleJ. Phys. A 39 (2006) 327-342
Document NumberSISSA;35/2005/FM

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.

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