Basic Methods Of Soliton Theory

By: Ivan V Cherednik

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Hardcover | 1 August 1996

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Hardcover
264 Pages

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22.86 x 16.51 x 1.91

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In the 25 years of its existence Soliton Theory has drastically expanded our understanding of “integrability” and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.Differential algebra (local conservation laws, Bäcklund-Darboux transforms), algebraic geometry (theta and Baker functions), and the inverse scattering method (Riemann-Hilbert problem) with well-grounded preliminaries are applied to various equations including principal chiral fields, Heisenberg magnets, Sin-Gordon, and Nonlinear Schrödinger equation.

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You Can Find This Book In

Non-Fiction Mathematics Geometry Algebraic Geometry Science Physics Classical Mathematics Wave Mechanics including Vibration & Acoustics Calculus & Mathematical Analysis Differential Calculus & Equations Applied Physics Applied Mathematics

Booktopia Publisher Services World Scientific Publishing Mathematical Physics

Preface
Introduction	p. 1
An outline of the main directions	p. 2
Conservation Laws and Algebraic-Geometric Solutions	p. 18
Local conservation laws	p. 20
Generalized Lax equations	p. 38
Algebraic-geometric solutions of basic equations	p. 62
Algebraic-geometric solutions of Sin-Gordon, NS, etc.	p. 89
Backlund Transforms and Inverse Problem	p. 113
Backlund transformations	p. 115
Introduction to the scattering theory	p. 148
Applications of the inverse problem method	p. 190
References	p. 239
Index	p. 249
Table of Contents provided by Blackwell. All Rights Reserved.

Basic Methods Of Soliton Theory

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