Painlevé equations and related topics : proceedings of the international conference, Saint Petersburg, Russia, June 17-23, 2011 / edited by Alexander D. Bruno, Alexander B. Batkhin.

Format:

Book

Contributor:

Bri︠u︡no, Aleksandr Dmitrievich.

Batkhin, Alexander B.

Series:

De Gruyter Proceedings in Mathematics

De Gruyter proceedings in mathematics

Language:

English

Subjects (All):

Painlevé equations--Congresses.

Painlevé equations.

Physical Description:

1 online resource (288 p.)

Edition:

1st ed.

Place of Publication:

Berlin : De Gruyter, [2012]

Language Note:

English

Summary:

This is a proceedings of the international conference "Painlevé Equations and Related Topics" which was taking place at the Euler International Mathematical Institute, a branch of the Saint Petersburg Department of the Steklov Institute of Mathematics of the Russian Academy of Sciences, in Saint Petersburg on June 17 to 23, 2011. The survey articles discuss the following topics: General ordinary differential equations Painlevé equations and their generalizations Painlevé property Discrete Painlevé equations Properties of solutions of all mentioned above equations:- Asymptotic forms and asymptotic expansions- Connections of asymptotic forms of a solution near different points- Convergency and asymptotic character of a formal solution- New types of asymptotic forms and asymptotic expansions- Riemann-Hilbert problems- Isomonodromic deformations of linear systems- Symmetries and transformations of solutions- Algebraic solutions Reductions of PDE to Painlevé equations and their generalizations Ordinary Differential Equations systems equivalent to Painlevé equations and their generalizations Applications of the equations and the solutions

Contents:

Front matter

Preface

Contents

Part I. Plane Power Geometry

Chapter 1. Plane Power Geometry for One ODE and P1-P6 / Bruno, Alexander D.

Chapter 2. New Simple Exact Solutions to Equation P6 / Batkhin, Alexander B. / Batkhina, Natalia V.

Chapter 3. Convergence of a Formal Solution to an ODE / Goryuchkina, Irina V.

Chapter 4. Asymptotic Expansions and Forms of Solutions to P6 / Goryuchkina, Irina V.

Chapter 5. Asymptotic Expansions of Solutions to P5 / Parusnikova, Anastasia V.

Part II. Space Power Geometry

Chapter 6. Space Power Geometry for one ODE and P1-P4, P6 / Bruno, Alexander D.

Chapter 7. Elliptic and Periodic Asymptotic Forms of Solutions to P5 / Bruno, Alexander D. / Parusnikova, Anastasia V.

Chapter 8. Regular Asymptotic Expansions of Solutions to One ODE and P1-P5 / Bruno, Alexander D.

Part III. Isomondromy Deformations

Chapter 9. Isomonodromic Deformations on Riemann Surfaces / Artamonov, Dmitry V.

Chapter 10. On Birational Darboux Coordinates of Isomonodromic Deformation Equations Phase Space / Babich, Mikhail V.

Chapter 11. On the Malgrange Isomonodromic Deformations of Nonresonant Irregular Systems / Bibilo, Yuliya P. / Gontsov, Renat R.

Chapter 12. Critical behavior of P6 Functions from the Isomonodromy Deformations Approach / Guzzetti, Davide

Chapter 13. Isomonodromy Deformation of the Heun Class Equation / Kazakov, Alexander Ya.

Chapter 14. Isomonodromy Deformations and Hypergeometric-Type Systems / Leksin, Vladimir P.

Chapter 15. A Monodromy Problem Connected with P6 / Novikov, Dmitrii P.

Chapter 16. Monodromy Evolving Deformations and Confluent Halphen's Systems / Ohyama, Yousuke

Chapter 17. On the Gauge Transformation of the Sixth Painlevé Equation / Sasaki, Yoshikatsu

Chapter 18. Expansions for Solutions of the Schlesinger Equation at a Singular Point / Vyugin, Ilya V.

Part IV. Painlevé Property

Chapter 19. Painleve Analysis of Lotka-Volterra Equations / Damianou, Pantelis A.

Chapter 20. Painlevé Test and Briot-Bouquet Systems / Gricuk, Evgenii / Gromak, Valerii

Chapter 21. Solutions of the Chazy System / Gromak, Valerii

Chapter 22. Third-Order Ordinary Differential Equations with the Painlevé Test / Adjabi, Yasin / Kessi, Arezki

Chapter 23. Analytic Properties of Solutions of a Class of Third-Order Equations with an Irrational Right-Hand Side / Martynov, Ivan P. / Pronko, Vyacheslav A. / Andreeva, Tatsyana K.

Part V. Other Aspects

Chapter 24. The Sixth Painlevé Transcendent and Uniformizable Orbifolds / Brezhnev, Yurii V.

Chapter 25. On Uniformizable Representation for Abelian Integrals / Brezhnev, Yurii V.

Chapter 26. Phase Shift for a Special Solution to the Korteweg-de Vries Equation in the Whitham Zone / Garifullin, Rustem N.

Chapter 27. Fuchsian Reduction of Differential Equations / Golubeva, Valentina A.

Chapter 28. The Voros Coefficient and the Parametric Stokes Phenomenon for the Second Painlevé Equation / Iwaki, Kohei

Chapter 29. Integral Symmetry and the Deformed Hypergeometric Equation / Kazakov, Alexander Ya.

Chapter 30. Integral Symmetries for Confluent Heun Equations and Symmetries of Painlevé Equation P5 / Kazakov, Alexander Ya. / Slavyanov, Sergey Yu.

Chapter 31. From the Tau Function of Painlevé P6 Equation to Moduli Spaces / Korotkin, Dmitry / Zograf, Peter

Chapter 32. On particular Solutions of q-Painlevé Equations and q-Hypergeometric Equations / Ohyama, Yousuke

Chapter 33. Derivation of Painlevé Equations by Antiquantization / Slavyanov, Sergey Yu.

Chapter 34. Integral Transformation of Heun's Equation and Apparent Singularity / Takemura, Kouichi

Chapter 35. Painlevé Analysis of Solutions to Some Nonlinear Differential Equations and their Systems Associated with Models of the Random-Matrix Type / Tsegel'nik, Vladimir

Chapter 36. Reductions on the Lattice and Painlevé Equations P2, P5, P6 / Xenitidis, Pavlos

Comments

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

1-283-62841-4

9786613940865

3-11-027566-X

OCLC:

812251499