2011/07/12 by V. E. Adler, V. V. Postnikov
Physics and Astronomy · Mathematics · #nlin.SI #math-ph #math.MP #msc:35Q53 #msc:37K10
paper · pdf · doi:10.1088/1751-8113/44/41/415203
published as J. Phys. A: Math. Theor. 44 (2011) 415203 · 23 pages, 2 figures
arxiv created 2011/07/12 · arxiv updated 2011/10/18
We study integrable hierarchies associated with spectral problems of the form Pψ=λQψ 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.