Lax pairs for additive difference Painlevé equations
Nagao, Hidehito
Exactly Solvable and Integrable Systems
Mathematical Physics
Classical Analysis and ODEs
14H70, 34M55, 37K20, 39A10, 41A05
Original · EN
A Lax pair for the additive difference Painlevé 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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