Conte R , Musette M The Painleve Handbook 2ed 2020 torrent

Textbook in PDF format

This book, now in its second edition, introduces the singularity analysis of differential and difference equations via the Painlevé test and shows how Painlevé analysis provides a powerful algorithmic approach to building explicit solutions to nonlinear ordinary and partial differential equations. It is illustrated with integrable equations such as the nonlinear Schrödinger equation, the Korteweg-de Vries equation, Hénon-Heiles type Hamiltonians, and numerous physically relevant examples such as the Kuramoto-Sivashinsky equation, the Kolmogorov-Petrovski-Piskunov equation, and mainly the cubic and quintic Ginzburg-Landau equations.
Extensively revised, updated, and expanded, this new edition includes: recent insights from Nevanlinna theory and analysis on both the cubic and quintic Ginzburg-Landau equations; a close look at physical problems involving the sixth Painlevé function; and an overview of new results since the book’s original publication with special focus on finite difference equations. The book features tutorials, appendices, and comprehensive references, and will appeal to graduate students and researchers in both mathematics and the physical sciences.

Introduction
Singularity Analysis: Painlevé Test
Integrating Ordinary Differential Equations
Partial Differential Equations: Painlevé Test
From the Test to Explicit Solutions of PDEs
Integration of Hamiltonian Systems
Discrete Nonlinear Equations
Selected Problems Integrated by Painlevé Functions
FAQ (Frequently Asked Questions)