Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2011-07-12
J. Phys. A: Math. Theor. 44 (2011) 415203
Nonlinear Sciences
Exactly Solvable and Integrable Systems
23 pages, 2 figures
Scientific paper
10.1088/1751-8113/44/41/415203
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.
Adler Vsevolod E.
Postnikov V. V.
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