Integrable Couplings, Variational Identities and Hamiltonian Formulations
نویسندگان
چکیده
We discuss Hamiltonian formulations for integrable couplings, particularly biand tri-integrable couplings, based on zero curvature equations. The basic tools are the variational identities over non-semisimple Lie algebras consisting of block matrices. Illustrative examples include dark equations and biand tri-integrable couplings of the KdV equation and the AKNS equations, generated from the enlarged matrix spectral problems. The associated variational identities yield bi-Hamiltonian formulations and hereditary recursion operators, thereby showing their Liouville integrability.
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