Painlevé analysis and its applications

Author(s)

• Chowdhury, A. R. (A. Roy)

Bibliographic Information

Painlevé analysis and its applications

A. Roy Chowdhury

（Chapman & Hall/CRC monographs and surveys in pure and applied mathematics, 105）

Chapman & Hall/CRC, c2000

Note

Includes bibliographical references (p. [286]-292) and index

Description and Table of Contents

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. 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.

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

by "Nielsen BookData"

Details

• NCID: BA45504678
• ISBN:
  • 0849306388
• LCCN: 99059342
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Boca Raton
• Pages/Volumes: 298 p.
• Size: 25 cm
• Subject Headings:
  • LCSH : Painlevé equations
• Parent Bibliography ID:
  • BA41758925