Overview

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. Painl?ve 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 Painlev? 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 Painlev? analysis and its practical applications. In it, the author addresses the soliton and nonlinearity, Painlev? analysis and the integrability of ordinary and partial differential equations, Painlev? properties, different forms of expansion, and the relation of Painlev? 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.P ainlev? 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.

Full Product Details

Author:   Amit K. Roy-Chowdhury (University of California, Riverside, USA)
Publisher:   Taylor & Francis Inc
Imprint:   CRC Press Inc
Volume:   105
Weight:   0.608kg
ISBN:  

9780849306389

ISBN 10:   0849306388
Pages:   312
Publication Date:   27 December 1999
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   Out of stock  

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 Painleve Analysis Painleve Property and ODEs Weak Painleve 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 Painleve Analysis of Perturbed Equations Painleve Analysis and Monodromy Matrix DISCRETE AND SOME SPECIAL SYSTEMS Painleve Test and Discrete System Long Wave/Short Wave Equation Fermionic System and Painleve Analysis Algebraic Intehgrability and Painleve Analysis Painleve Analysis of Some Special Systems MISCELLANEOUS IDEAS IN RELATION TO PAINLEVE ANALYSIS Geometry and Painleve Analysis Generation of a Higher Dimensional System from a Lower Dimensional System Conformal Symmetry, Painleve Test, and Infinite Number of Symmetries Painleve Analysis and Painleve Equations The Ablowita, Ramani, Segur Approach Painleve Analysis of Hierarchy Lax Type Representation of Painleve Equation Possibility of Leading Positive Exponent REFERENCES

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Roy-Chowdhury\, Amit K.

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