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

Buch 3 von 24: Mathematical Physics Studies

Gu, Chaohao; Hu, Anning; Zhou, Zixiang

 
9789048167883: Darboux Transformations in Integrable Systems: Theory and their Applications to Geometry (Mathematical Physics Studies, Band 26)
Softcover
ISBN 10: 9048167884 ISBN 13: 9789048167883
Verlag: Springer, 2010

Inhaltsangabe

1+1 Dimensional Integrable Systems.- 2+1 Dimensional Integrable Systems.- N + 1 Dimensional Integrable Systems.- Surfaces of Constant Curvature, Bäcklund Congruences and Darboux Transformation.- Darboux Transformation and Harmonic Map.- Generalized Self-Dual Yang-Mills Equations and Yang-Mills-Higgs Equations.- Two Dimensional Toda Equations and Laplace Sequences of Surfaces in Projective Space.

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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.

Audience:

The book has been written for specialists, teachers and graduate students (or undergraduate students of higher grade) in mathematics and physics.

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Verlag
Springer
Erscheinungsdatum
2010
Sprache
Englisch
ISBN 10 
9048167884
ISBN 13 
9789048167883
Einband
Taschenbuch
Anzahl der Seiten
320
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Weitere beliebte Ausgaben desselben Titels

9781402030871: Darboux Transformations in Integrable Systems: Theory and their Applications to Geometry (Mathematical Physics Studies, 26, Band 25)

Vorgestellte Ausgabe

ISBN 10:  1402030878 ISBN 13:  9781402030871
Verlag: Springer, 2004
Hardcover