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OverviewThe 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 DetailsAuthor: Chaohao Gu , Anning Hu , Zixiang ZhouPublisher: 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: 9789048167883ISBN 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  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of Contents1+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.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) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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