Painleve Analysis and Its Applications: 1st Edition (Hardback) book cover

Painleve Analysis and Its Applications

1st Edition

By Amit K. Roy-Chowdhury

Chapman and Hall/CRC

312 pages

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Hardback: 9780849306389
pub: 1999-12-27
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Description

With interest in the study of nonlinear systems at an all-time high, researchers are eager to explore the mysteries behind the nonlinear equations that govern various physical processes. Painléve analysis may be the only tool available that allows the analysis of both integrable and non-integrable systems.

With a primary objective of introducing the uninitiated to the various techniques of the Painlevé approach, this monograph brings together the results of the extensive research performed in the field over the last few decades. For the first time in a single volume, this book offers treatment of both the theory of Painlevé analysis and its practical applications. In it, the author addresses the soliton and nonlinearity, Painlevé analysis and the integrability of ordinary and partial differential equations, Painlevé properties, different forms of expansion, and the relation of Painlevé expansion with conformal invariance. He also gives a detailed account of negative resonances, explains the connection with monodromy, and demonstrates applications to specific important equations.

Painlevé Analysis and Its Applications offers a clear presentation and down-to-earth approach that includes many examples and requires only a basic understanding of complex function theory and differential equations.

Table of Contents

NONLINEARITY AND INTEGRABILITY

Soliton and Nonlinearity

Some of the Important Approaches for Getting Information Regarding a Given nPDE

BASIC IDEAS AND METHODS

Painlevé Analysis

Painlevé Property and ODEs

Weak Painlevé Property and ODEs

CONFORMAL INVARIANCE

Introduction

KdV Revisited Boussinesq Equation

Kowalievski's Exponent Integrals of Motion

Nonintegrable Systems and Painleve Analysis

Painleve Analysis in more than (1+1) Dimensions

Negative Resonance and Painleve Expansion

Painlevé Analysis of Perturbed Equations

Painlevé Analysis and Monodromy Matrix

DISCRETE AND SOME SPECIAL SYSTEMS

Painlevé Test and Discrete System

Long Wave/Short Wave Equation

Fermionic System and Painlevé Analysis

Algebraic Intehgrability and Painlevé Analysis

Painlevé Analysis of Some Special Systems

MISCELLANEOUS IDEAS IN RELATION TO PAINLEVE ANALYSIS

Geometry and Painlevé Analysis

Generation of a Higher Dimensional System from a Lower Dimensional System

Conformal Symmetry, Painlevé Test, and Infinite Number of Symmetries

Painlevé Analysis and Painlevé Equations

The Ablowita, Ramani, Segur Approach

Painlevé Analysis of Hierarchy

Lax Type Representation of Painlevé Equation

Possibility of Leading Positive Exponent

REFERENCES

About the Series

Monographs and Surveys in Pure and Applied Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations