Painlevé analysis and its applications
著者
書誌事項
Painlevé analysis and its applications
（Chapman & Hall/CRC monographs and surveys in pure and applied mathematics, 105）
Chapman & Hall/CRC, c2000
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注記
Includes bibliographical references (p. [286]-292) and index
内容説明・目次
内容説明
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. Painleve 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 Painleve 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 Painleve analysis and its practical applications. In it, the author 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. He also gives a detailed account of negative resonances, explains the connection with monodromy, and demonstrates applications to specific important equations.
Painleve 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.
目次
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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