Generalized Volterra lattices: binary Darboux transformations and   self-consistent sources
  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. 
Folkert M\"uller-Hoissen, Oleksandr Chvartatskyi, Kouichi Toda
nlin.SI math-ph math.MP