Differentialdifference equations associated with the fractional Lax operators
Abstract
We study integrable hierarchies associated with spectral problems of the form Pψ = λQψ, where P and Q are difference operators. The corresponding nonlinear differentialdifference equations can be viewed as inhomogeneous generalizations of the Bogoyavlenskytype lattices. While the latter turn into the Kortewegde Vries equation under the continuous limit, the lattices under consideration provide discrete analogs of the SawadaKotera and KaupKupershmidt equations. The rmatrix formulation and several of the simplest explicit solutions are presented.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 October 2011
 DOI:
 10.1088/17518113/44/41/415203
 arXiv:
 arXiv:1107.2305
 Bibcode:
 2011JPhA...44O5203A
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics;
 35Q53;
 37K10
 EPrint:
 23 pages, 2 figures