Differential-difference equations associated with the fractional Lax   operators
  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. 
V.E. Adler, V.V. Postnikov
nlin.SI math-ph math.MP