ENGLISH

Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models

By Fritz Gesztesy , Helge Holden

Book information

Publisher
Cambridge University Press
Year
2003
ISBN
0521753074, 9780521753074, 9780511066573
Language
english
Format
PDF
Filesize
3 MB (2858358 bytes)
Series
Cambridge Studies in Advanced Mathematics 79
Pages
519\519
Scanned
yes
Time added
2010-10-13 10:14:08

Description

This book is about algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions; also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sine-Gordon, and Camassa-Holm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebro-geometric solutions in the stationary and time-dependent contexts is provided. The formalism presented includes trace formulas, Dubrovin-type initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces).

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