ENGLISH

Darboux Transformations in Integrable Systems: Theory and their Applications to Geometry (Mathematical Physics Studies, 26)

By Chaohao Gu , Hesheng Hu , Zixiang Zhou,

Book information

Year
2005
ISBN
1402030878, 9781402030888, 9781402030871
Open Library ID
OL18228149M
Language
english
Format
PDF
Filesize
7 MB (7237372 bytes)
Edition
1
Pages
317\317
Scanned
yes
Time added
2011-06-04 13:46:07
Математика;Математическая физика

Description

The Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play important roles in mechanics, physics and differential geometry. This book presents the Darboux transformations in matrix form and provides purely algebraic algorithms for constructing the explicit solutions. A basis for using symbolic computations to obtain the explicit exact solutions for many integrable systems is established. Moreover, the behavior of simple and multi-solutions, even in multi-dimensional cases, can be elucidated clearly. The method covers a series of important equations such as various kinds of AKNS systems in R1+n, harmonic maps from 2-dimensional manifolds, self-dual Yang-Mills fields and the generalizations to higher dimensional case, theory of line congruences in three dimensions or higher dimensional space etc. All these cases are explained in detail. This book contains many results that were obtained by the authors in the past few years.

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