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On fourth-order nonlinear differential equations with the Painlevé property

On fourth-order nonlinear differential equations with the Painlevé property ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 8, pp. 1076–1085.  c Pleiades Publishing, Inc., 2006. Original Russian Text  c V.I. Gromak, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 8, pp. 1017–1026. ORDINARY DIFFERENTIAL EQUATIONS On Fourth-Order Nonlinear Differential Equations with the Painlev´ e Property V. I. Gromak Belarus State University, Minsk, Belarus Received April 25, 2005 DOI: 10.1134/S0012266106080027 1. INTRODUCTION Properties of solutions of Painlev´ e equations were studied from various viewpoints (e.g., see [1–18]). The Painlev´ e equations were originally obtained from the Painlev´ e classification of second- order ordinary differential equations without movable critical points [1] (the Painlev´ e property). Now they are widely used in the theory of isomonodromic deformations of linear systems [13, 14], the theory of Abelian integrals and algebraic geometry [19], theory of random matrices, and various physical applications (e.g., see [2, 6, 8, 13–17]). The problem on conditions guaranteeing the Painlev´ e property can be considered for higher-order ordinary differential equations as well, but there is no complete classification of such equations. Painlev´ e equations and higher-order Painlev´ e- like equations naturally arise from symmetric reductions of integrable nonlinear partial differential equations, which, in particular, is one http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

On fourth-order nonlinear differential equations with the Painlevé property

Gromak, V.
Differential Equations , Volume 42 (8) – Oct 7, 2006
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References (25)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Pleiades Publishing, Inc.
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266106080027
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 8, pp. 1076–1085.  c Pleiades Publishing, Inc., 2006. Original Russian Text  c V.I. Gromak, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 8, pp. 1017–1026. ORDINARY DIFFERENTIAL EQUATIONS On Fourth-Order Nonlinear Differential Equations with the Painlev´ e Property V. I. Gromak Belarus State University, Minsk, Belarus Received April 25, 2005 DOI: 10.1134/S0012266106080027 1. INTRODUCTION Properties of solutions of Painlev´ e equations were studied from various viewpoints (e.g., see [1–18]). The Painlev´ e equations were originally obtained from the Painlev´ e classification of second- order ordinary differential equations without movable critical points [1] (the Painlev´ e property). Now they are widely used in the theory of isomonodromic deformations of linear systems [13, 14], the theory of Abelian integrals and algebraic geometry [19], theory of random matrices, and various physical applications (e.g., see [2, 6, 8, 13–17]). The problem on conditions guaranteeing the Painlev´ e property can be considered for higher-order ordinary differential equations as well, but there is no complete classification of such equations. Painlev´ e equations and higher-order Painlev´ e- like equations naturally arise from symmetric reductions of integrable nonlinear partial differential equations, which, in particular, is one

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Differential Equations – Springer Journals

Published: Oct 7, 2006

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