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PRINTED BOOKS
Author Roy Chowdhury, A. (Asesh)

Title Painlevé analysis and its applications / A. Roy Chowdhury.

Published Boca Raton, FL : Chapman & Hall/CRC, [2000]
©2000

Copies

Location Call No. Status
 UniM ERC  515.39 CHOW    AVAILABLE
Physical description 298 pages ; 25 cm.
Series Monographs and surveys in pure and applied mathematics ; 105.
Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ; 105.
Bibliography Includes bibliographical references (pages [286]-292) and index.
Contents Chapter 1 Nonlinearity and Integrability 1 -- 1.1 Soliton and Nonlinearity 1 -- 1.2 Some of the Important Approaches for Getting Information Regarding a Given nPDE 5 -- Chapter 2 Basic Ideas and Methods 7 -- 2.1 Painleve Analysis 7 -- 2.2 Painleve Property and ODE's 18 -- 2.3 Weak Painleve Property and ODE's 26 -- Chapter 3 Conformal Invariance 28 -- 3.2 KdV Revisited 35 -- 3.3 Boussinesq Equation 38 -- 3.4 Kowalevski's Exponent Integrals of Motion 45 -- 3.5 Nonintegrable System and Painleve Analysis 56 -- 3.6 Painleve Analysis in more than (1+1) Dimension 91 -- 3.7 Negative Resonance and Painleve Expansion 109 -- 3.8 Painleve Analysis of Perturbed Equation 120 -- 3.9 Painleve Analysis and Mondromy Matrix 125 -- Chapter 4 Discrete and Some Special Systems 147 -- 4.1 Painleve Test and Discrete System 147 -- 4.2 Long Wave/Short Wave Equation 173 -- 4.3 Fermionic System and Painleve Analysis 186 -- 4.4 Algebraic Integrability and Painleve Analysis 192 -- 4.5 Painleve Analysis of Some Special Systems 209 -- Chapter 5 Miscellaneous Ideas in Relation to Painleve Analysis 236 -- 5.1 Geometry and Painleve Analysis 236 -- 5.2 Generation of a Higher Dimensional System from a Lower Dimensional System 241 -- 5.3 Conformal Symmetry, Painleve Test, and Infinite Number of Symmetries 245 -- 5.4 Painleve Analysis and Painleve Equations 247 -- 5.5 Ablowitz, Ramani, Segur Approach 250 -- 5.6 Painleve Analysis of Hierarchy 258 -- 5.7 Lax Type Representation of Painleve Equation 269 -- 5.8 Possibility of Leading Positive Exponent 275.
Summary Introduces various techniques of the Painleve approach and discusses the theory behind it and its practical applications. Addresses the soliton and nonlinearity, Painleve analysis and the integrability of ordinary and partial differential equations, Painleve properties, different forms of expansion, and the relation of Painleve expansion with conformal invariance. Also gives a detailed account of negative resonances, and demonstrates applications to specific important equations.
Subject Painlevé equations.
ISBN 0849306388 (alk. paper)