Generalized Volterra lattices: binary Darboux transformations and self-consistent sources

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.

2nd version: several corrections and additions, 24 pages, 4 figures, to appear in Journal of Geometry and Physics

References in corpus (3)

• Integrable Möbius invariant evolutionary lattices of second order
• Binary Darboux Transformations in Bidifferential Calculus and Integrable Reductions of Vacuum Einstein Equations
• Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations