1209.4721 (C. M. Ormerod et al.)

On Lax representations of reductions of integrable lattice equations    [PDF]

C. M. Ormerod, P. H. van der Kamp, G. R. W. Quispel

We present a method of determining a Lax representation for similarity reductions of autonomous and non-autonomous partial difference equations. This method may be used to obtain Lax representations that are general enough to provide the Lax integrability for entire hierarchies of reductions. A main result is, as an example of this framework, how we may obtain the $q$-Painlev\'e equation whose group of B\"acklund transformations is an affine Weyl group of type $E_6^{(1)}$ as a similarity reduction of the discrete Schwarzian Korteweg-de Vries equation.

View original: http://arxiv.org/abs/1209.4721