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
大学図書館所蔵 全31件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
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
「Nielsen BookData」 より