Mathematics-Geometry and Topology

Darboux transformations in integrable systems: theory and their applications to geometry

US$5.00 US$63.00

Title (user) : Darboux transformations in integrable systems: theory and their applications to geometryTitle (google) : Darboux Transformations in Integrable Systems Theory and their Applications to GeometryISBN : 140203087...
Description

Title (user) : Darboux transformations in integrable systems: theory and their applications to geometry

Title (google) : Darboux Transformations in Integrable Systems Theory and their Applications to Geometry

ISBN : 1402030878,9781402030888,9781402030871,1402030886

ISSN : 0921-3767

GoogleBook ID : A_oWEsiJKRwC

OpenLibrary ID : OL18228149M

Edition : 1

Series : Mathematical physics studies 26

Authors (user) : Chaohao Gu, H. Hu, Zixiang Zhou

Authors (google) : Chaohao Gu,Anning Hu,Zixiang Zhou

Publisher : Springer

Language : English

Publication Date : 2004

Scanned : yes (600 DPI)

File Format : djvu

Categories : Science


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Description (user) :

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.

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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Description (google) :
Annotation. Contributors1. Introduction: Towards an Emergentist Worldview, Paul DaviesPART I. DEFINING COMPLEXITY2. Randomness and Mathematical Proof, Gregory J. Chaitin3. How to Define Complexity in Physics, and Why, Charles H. BennettPART II. THE CONCEPT OF INFORMATION IN PHYSICS AND BIOLOGY4. The Emergence of Autonomous Agents, Stuart Kauffman5. Complexity and the Arrow of Time, Paul Davies6. Can Evolutionary Algorithms Generate Specified Complexity?, William A. Dembski7. The Second Law of Gravutucs and the Fourth Law of Thermodynamics, Ian Stewart8. Two Arros from a Mighty Bow, Werner R. LoewensteinPART III. PHILOSOPHICAL AND RELIGIOUS PERSPECTIVES9. Emergence of Transcendence, Harold J. Morowitz10. Complexity, Emergence, and Divine Creativity, Arthur Peacocke11. From Anthropic Design to Self-Organized Complexity, Niels Henrik GregersenIndex.

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