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

DOI10.2969/jmsj/06430733zbMath1255.39016OpenAlexW2026185435MaRDI QIDQ455001

Shun Shimomura

Publication date: 2 October 2012

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jmsj/1343133742

zbMATH Keywords

asymptotic solutionsecond Painlevé equationcontinuous limitdifference second Painlevé equation

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 (4)

Meromorphic solutions of algebraic difference equations ⋮ Meromorphic solutions of difference Riccati equations ⋮ Nonlinear q-Stokes phenomena for q-Painlevé I ⋮ Asymptotic solutions of the discrete Painlevé equation of second type

Cites Work

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• Rational solutions of difference Painlevé equations
• From continuous to discrete Painlevé equations
• Discrete Painlevé equations: coalescences, limits and degeneracies
• Rational solutions for the discrete Painlevé II equation.
• Meromorphic solutions of difference Painlevé equations
• Miura transforms for discrete Painleve equations
• Discrete versions of the Painlevé equations
• Bilinear discrete Painleve-II and its particular solutions
• Quasi-linear Stokes phenomenon for the second Painlev  transcendent

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