English

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

Exactly Solvable and Integrable Systems 2017-03-08 v2 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.1606.03744,
  title  = {Generalized Volterra lattices: binary Darboux transformations and self-consistent sources},
  author = {Folkert Müller-Hoissen and Oleksandr Chvartatskyi and Kouichi Toda},
  journal= {arXiv preprint arXiv:1606.03744},
  year   = {2017}
}

Comments

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

R2 v1 2026-06-22T14:23:29.932Z