Lax pairs for additive difference Painlevé equations

Hidehito Nagao

paper

Lax pairs for additive difference Painlevé equations

arXiv:1604.02530

Abstract

A Lax pair for the additive difference Painlevé equation of type $E_{7}^{(1)}$ is explicitly obtained as certain linear difference equations of scalar form. The compatibility of the Lax pair is proved by using certain characterization of the coefficients in the Lax equation. Some Lax pairs for types $E_{6}^{(1)}$ , $D_{4}^{(1)}$ and $A_{3}^{(1)}$ are also given by the degeneration.

9 pages, 2 figures, 1 table