Lax pairs for additive difference Painlevé equations

2016/04/09 by Hidehito Nagao, Nagao, Hidehito
Computer Science · Mathematics · Physics and Astronomy · #14H70 #34M55 #37K20 #39A10 #41A05 #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1604.02530

openalex publication_date 2016/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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