Bi-integrable and tri-integrable couplings of a soliton hierarchy associated with SO(4)

Abstract

In our paper, the theory of bi-integrable and tri-integrable couplings is generalized to the discrete case. First, based on the six-dimensional real special orthogonal Lie algebra SO(4), we construct bi-integrable and tri-integrable couplings associated with SO(4) for a hierarchy from the enlarged matrix spectral problems and the enlarged zero curvature equations. Moreover, Hamiltonian structures of the obtained bi-integrable and tri-integrable couplings are constructed by the variational identities.

Keywords

• bi-integrable couplings
• tri-integrable couplings
• zero curvature equations
• hamiltonian structures
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