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Constructing nonlinear discrete integrable Hamiltonian couplings. (English) Zbl 1205.37085
Summary: Beginning with Lax pairs from special non-semisimple matrix Lie algebras, we establish a scheme for constructing nonlinear discrete integrable couplings. Discrete variational identities over the associated loop algebras are used to build Hamiltonian structures for the resulting integrable couplings. We illustrate the application of the scheme by means of an enlarged Volterra spectral problem and present an example of nonlinear discrete integrable Hamiltonian couplings for the Volterra lattice equations.

MSC:
37K60 Lattice dynamics; integrable lattice equations
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
39A70 Difference operators
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