Painlevé Differential Equations in the Complex Plane

Nachdruck 2013
ISBN: 978-3-11-017379-6
Verlag: De Gruyter

Buch, Englisch, Band 28, 303 Seiten, Format (B × H): 175 mm x 246 mm, Gewicht: 711 g

Reihe: De Gruyter Studies in Mathematics

This book is the first comprehensive treatment of Painlevé differential equations in the complex plane. Starting with a rigorous presentation for the meromorphic nature of their solutions, the Nevanlinna theory will be applied to offer a detailed exposition of growth aspects and value distribution of Painlevé transcendents. The subsequent main part of the book is devoted to topics of classical background such as representations and expansions of solutions, solutions of special type like rational and special transcendental solutions, Bäcklund transformations and higher order analogues, treated separately for each of these six equations. The final chapter offers a short overview of applications of Painlevé equations, including an introduction to their discrete counterparts. Due to the present important role of Painlevé equations in physical applications, this monograph should be of interest to researchers in both mathematics and physics and to graduate students interested in mathematical physics and the theory of differential equations.

Zielgruppe

Researchers in Mathematics and Physics, Graduate Students

Autoren/Hrsg.

Gromak, Valerii I.

Shimomura, Shun

Laine, Ilpo

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Frontmatter
Contents
Chapter 1. Meromorphic nature of solutions
Chapter 2. Growth of Painlevé transcendents
Chapter 3. Value distribution of Painlevé transcendents
Chapter 4. The first Painlevé equation (P1)
Chapter 5. The second Painlevé equation (P2)
Chapter 6. The fourth Painlevé equation (P4)
Chapter 7. The third Painlevé equation (P3)
Chapter 8. The fifth Painlevé equation (P5)
Chapter 9. The sixth Painlevé equation (P6)
Chapter 10. Applications of Painlevé equations
Appendix A. Local existence and uniqueness of solutions of complex differential equations
Appendix B. Basic notations and facts in the Nevanlinna theory
Backmatter

Über Autor(innen)

Laine, Ilpo
Ilpo Laine is Professor at the Mathematics Department of the University of Joensuu, Finland.

Gromak, Valerii I.
Dr. Valerii Gromak works at the Belarussian State University in Minsk, Belarussia.

Shimomura, Shun
Shun Shimomura is Professor at the Mathematics Department of Keio University, Yokohama, Japan.

Dr. Valerii Gromak works at the Belarussian State University in Minsk, Belarussia. Ilpo Laine is Professor at the Mathematics Department of the University of Joensuu, Finland. Shun Shimomura is Professor at the Mathematics Department of Keio University, Yokohama, Japan.