Lax pairs for additive difference Painlev\'e equations
Abstract
A Lax pair for the additive difference Painlev\'e equation of type E7(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 E6(1), D4(1) and A3(1) are also given by the degeneration.
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