Differential-difference equations associated with the fractional Lax operators

V. E. Adler; V. V. Postnikov

doi:10.1088/1751-8113/44/41/415203

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arXiv · 1107.2305

Differential-difference equations associated with the fractional Lax operators

V. E. Adler·V. V. Postnikov

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Abstract

We study integrable hierarchies associated with spectral problems of the form $P\psi=\lambda Q\psi$ where $P,Q$ are difference operators. The corresponding nonlinear differential-difference equations can be viewed as inhomogeneous generalizations of the Bogoyavlensky type lattices. While the latter turn into the Korteweg--de Vries equation under the continuous limit, the lattices under consideration provide discrete analogs of the Sawada--Kotera and Kaup--Kupershmidt equations. The $r$-matrix formulation and several simplest explicit solutions are presented.

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BibTeX RIS

V. E. Adler, V. V. Postnikov. 2011-07-12. Differential-difference equations associated with the fractional Lax operators. https://doi.org/10.1088/1751-8113/44/41/415203

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