A study of the discrete \(P_ V\) equation: Miura transformations and particular solutions

DOI10.1007/BF00398353zbMath0863.39004OpenAlexW2092846055MaRDI QIDQ1816426

K. M. Tamizhmani, Yasuhiro Ohta, Alfred Ramani, Basile Grammaticos

Publication date: 8 June 1997

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00398353

zbMATH Keywords

rational solutionsMiura transformationdiscrete Painlevé equationsauto-Bäcklund transformationSchlesinger transformationssolutions involving discrete confluent hypergeometric (Whittaker) functions

Mathematics Subject Classification ID

Topological dynamics (37B99) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Other functions coming from differential, difference and integral equations (33E30) Additive difference equations (39A10)

Related Items (4)

A bilinear approach to discrete Miura transformations. ⋮ Proceedings of the 12th international workshop on nonlinear evolution equations and dynamical systems (NEEDS '98), Leeds, UK, June 21--28, 1998. Transl. from the Russian ⋮ A simplified version of higher covariant derivative regularization ⋮ Bäcklund transformations for discrete Painlevé equations: discrete P\(_{\text{II}}\)-P\(_{\text{V}}\)

Cites Work

• Schlesinger transforms for the discrete Painlevé IV equation
• Integrable mappings and soliton equations. II
• Discrete Painlevé equations: coalescences, limits and degeneracies
• Discrete versions of the Painlevé equations
• Do integrable mappings have the Painlevé property?
• On a unified approach to transformations and elementary solutions of Painlevé equations
• Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
• Linearization and solutions of the discrete Painlevé III equation

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