Basic Methods Of Soliton Theory: 25 (Advanced Series In Mathematical Physics) - Softcover

Cherednik, Ivan

Softcover

ISBN 10: 9810226438 ISBN 13: 9789810226435

Publisher: Wspc, 1996

Synopsis

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.

About this title

Synopsis

This text is a introduction to the mathematical soliton theory with an emphasis on algebraic aspects, including an exposition of its background, the recent developments and concrete methods for the equations important to physics. The book is centered around general matrix soliton equation, which are of importance to the foundations and applications of soliton theory. It contains algebraized constructions of local conservation laws; Backlund-Darboux transformations; the integration technique by algebraic geometry and the inverse scattering method and the Hamiltonian theory with well grounded preliminaries. The general results are detailed for the Sine-Gordon, Nonlinear Schrodinger, Landau-Lifschitz equations and are interpreted from the point of view of algebraic geometry and the representaion theory by means of loop groups and Kac-Moody algebras, r-matrices and tau-functions.

Edition details

• Publisher: Wspc
• Publication date: 1996
• Language: English
• ISBN 10: 9810226438
• ISBN 13: 9789810226435
• Binding: Paperback
• Number of pages: 262