Overview
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.
Full Product Details
Author: Chaohao Gu ,
Anning Hu ,
Zixiang Zhou
Publisher: Springer
Imprint: Springer
Edition: Softcover reprint of hardcover 1st ed. 2005
Volume: 26
Dimensions:
Width: 16.00cm
, Height: 1.70cm
, Length: 24.00cm
Weight: 0.514kg
ISBN: 9789048167883
ISBN 10: 9048167884
Pages: 308
Publication Date: 28 October 2010
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Out of stock
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Reviews
From the reviews: ""The book is concerned with mutual relations between the differential geometry of surfaces and the theory of integrable nonlinear systems of partial differential equations. It concentrates on the Darboux matrix method for constructing explicit solutions to various integrable nonlinear PDEs. … This book can be recommended for students and researchers who are interested in a differential-geometric approach to integrable nonlinear PDE’s."" (Jun-ichi Inoguchi, Mathematical Reviews, Issue 2006 i)
"From the reviews: ""The book is concerned with mutual relations between the differential geometry of surfaces and the theory of integrable nonlinear systems of partial differential equations. It concentrates on the Darboux matrix method for constructing explicit solutions to various integrable nonlinear PDEs. … This book can be recommended for students and researchers who are interested in a differential-geometric approach to integrable nonlinear PDE’s."" (Jun-ichi Inoguchi, Mathematical Reviews, Issue 2006 i)"
From the reviews: The book is concerned with mutual relations between the differential geometry of surfaces and the theory of integrable nonlinear systems of partial differential equations. It concentrates on the Darboux matrix method for constructing explicit solutions to various integrable nonlinear PDEs. ! This book can be recommended for students and researchers who are interested in a differential-geometric approach to integrable nonlinear PDE's. (Jun-ichi Inoguchi, Mathematical Reviews, Issue 2006 i)
