Exact solutions of a q -discrete second Painlevé equation from its iso-monodromy deformation problem: I. Rational solutions

DOI10.1098/rspa.2011.0167zbMath1243.39008OpenAlexW2159864947MaRDI QIDQ2901814

Nalini Joshi, Yang Shi

Publication date: 31 July 2012

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2011.0167

zbMATH Keywords

Painlevé equationsspecial solutionsiso-monodeomy deformation

Mathematics Subject Classification ID

Difference equations, scaling ((q)-differences) (39A13) Painlevé-type functions (33E17)

Related Items (3)

Difference integrability conditions for parameterized linear difference and differential equations ⋮ Hierarchies of q-discrete Painlevé equations ⋮ Asymptotics and confluence for a singular nonlinear \(q\)-difference-differential Cauchy problem

Cites Work

• Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\)
• Monodromy- and spectrum-preserving deformations. I
• Rational surfaces associated with affine root systems and geometry of the Painlevé equations
• A bilinear approach to discrete Miura transformations.
• A differential equation for orthogonal polynomials
• A Lax pair for a lattice modified KdV equation, reductions toq-Painlevé equations and associated Lax pairs
• Lax forms of theq-Painlevé equations
• On a q-Difference Painlevé III Equation: II. Rational Solutions
• Discrete versions of the Painlevé equations
• On a q-Difference Painlevé III Equation: I. Derivation, Symmetry and Riccati Type Solutions
• Projective Reduction of the Discrete Painleve System of Type (A2 + A1)(1)
• Rational Solutions of Painlevé Equations

This page was built for publication: Exact solutions of a q -discrete second Painlevé equation from its iso-monodromy deformation problem: I. Rational solutions