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Bidifferential calculus; Darboux transformation; Self-consistent sources; Volterra lattice; Bogoyavlensky lattices
Abstract:
We study two families of matrix versions of generalized Volterra (or Bogoyavlensky) lattice equations. For each family, the equations arise as reductions of a partial differential–difference equation in one continuous and two discrete variables, which is a realization of a general integrable equation in bidifferential calculus. This allows to derive a binary Darboux transformation and also self-consistent source extensions via general results of bidifferential calculus. Exact solutions are constructed from the simplest seed solutions.
