English

Lax pairs for additive difference Painlev\'e equations

Exactly Solvable and Integrable Systems 2016-04-13 v1 Mathematical Physics Classical Analysis and ODEs math.MP

Abstract

A Lax pair for the additive difference Painlev\'e equation of type E7(1)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 E6(1)E_6^{(1)}, D4(1)D_4^{(1)} and A3(1)A_3^{(1)} are also given by the degeneration.

Cite

@article{arxiv.1604.02530,
  title  = {Lax pairs for additive difference Painlev\'e equations},
  author = {Hidehito Nagao},
  journal= {arXiv preprint arXiv:1604.02530},
  year   = {2016}
}

Comments

9 pages, 2 figures, 1 table

R2 v1 2026-06-22T13:28:30.611Z