Rational solutions of difference Painlevé equations

DOI10.3836/tjm/1342701346zbMath1259.39014OpenAlexW2060007591MaRDI QIDQ447806

Shun Shimomura

Publication date: 29 August 2012

Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.tjm/1342701346

zbMATH Keywords

rational solutionsdiscrete Painlevé equationauto-Bäcklund transformationautonomous casesdifference Painlevé equationsnon-autonomous cases

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Discrete version of topics in analysis (39A12) Multiplicative and other generalized difference equations (39A20) Difference equations in the complex domain (39A45)

Related Items (1)

Continuous limit of the difference second Painlevé equation and its asymptotic solutions

Cites Work

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• From continuous to discrete Painlevé equations
• Integrable mappings and soliton equations
• Discrete Painlevé equations: coalescences, limits and degeneracies
• Rational solutions for the discrete Painlevé II equation.
• Existence of finite-order meromorphic solutions as a detector of integrability in difference equations
• Miura transforms for discrete Painleve equations
• Casorati determinant solutions for the discrete Painleve-II equation
• Discrete versions of the Painlevé equations
• Bilinear discrete Painleve-II and its particular solutions
• On the autonomous limit of discrete Painlevé equations

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