Classical solutions of the third Painlevé equation

DOI10.1017/S0027763000005298zbMath0846.34002OpenAlexW1493614156MaRDI QIDQ4869959

Yoshihiro Murata

Publication date: 22 September 1996

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0027763000005298

zbMATH Keywords

classical solutionsirreducibilitythird Painlevé equation

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Other functions coming from differential, difference and integral equations (33E30)

Related Items (25)

Painlevé equations -- nonlinear special functions. ⋮ Classical solutions of the degenerate fifth Painlevé equation ⋮ On transformations in the Painlevé family ⋮ The fourth Painlevé equation and associated special polynomials ⋮ Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations ⋮ On a surface isolated by Gambier ⋮ On a distinguished family of random variables and Painlevé equations ⋮ A constructive proof for the Umemura polynomials of the third Painlevé equation ⋮ Generic differential equations are strongly minimal ⋮ Algebraic independence of generic Painlevé transcendents: PIII and PVI ⋮ Single-user MIMO system, Painlevé transcendents, and double scaling ⋮ On the Umemura polynomials for the Painlevé III equation ⋮ The Symmetric Fourth Painlevé Hierarchy and Associated Special Polynomials ⋮ Solutions of the second and fourth Painlevé equations, I ⋮ Special polynomials associated with rational solutions of the fifth Painlevé equation ⋮ Hierarchies of exact solutions for the discrete third Painlevé equation ⋮ On a q-Difference Painlevé III Equation: II. Rational Solutions ⋮ New transformations for Painlevé’s third transcendent ⋮ Rational solutions of the classical Boussinesq system ⋮ 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 ⋮ On the algebraic solutions of the Painlevé-III (\(\mathrm{D}_7\)) equation ⋮ RATIONAL SOLUTIONS OF THE BOUSSINESQ EQUATION ⋮ Specialisation of the Galois groupoid of a vector field ⋮ Solutions of the third Painlevé equation I ⋮ On the algebraic independence of generic Painlevé transcendents

Cites Work

• Polynomial Hamiltonians associated with Painleve equations. I
• Birational automorphism groups and differential equations
• A note on the transcendency of Painlevé’s first transcendent

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