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arXiv · 1606.03744

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

Folkert Müller-Hoissen·Oleksandr Chvartatskyi·Kouichi Toda
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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.

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Folkert Müller-Hoissen, Oleksandr Chvartatskyi, Kouichi Toda. 2016-06-12. Generalized Volterra lattices: binary Darboux transformations and self-consistent sources. https://doi.org/10.1016/j.geomphys.2016.11.026

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