Koha online

Your cart is empty.
Normal view MARC view ISBD view

Darboux Transformations in Integrable Systems [electronic resource] :Theory and their Applications to Geometry / by Chaohao Gu, Hesheng Hu, Zixiang Zhou.

by Gu, Chaohao [author.]; Hu, Hesheng [author.]; Zhou, Zixiang [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Mathematical Physics Studies: 26Publisher: Dordrecht : Springer Netherlands : 2005.Description: X, 310 p. online resource.ISBN: 9781402030888.Subject(s): Physics | Global differential geometry | Mathematical physics | Physics | Theoretical, Mathematical and Computational Physics | Mathematical Methods in Physics | Differential GeometryDDC classification: 530.1 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
Tags from this library: No tags from this library for this title. Add tag(s)
Log in to add tags.
    average rating: 0.0 (0 votes)

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.

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.

There are no comments for this item.

Log in to your account to post a comment.
@ Jomo Kenyatta University Of Agriculture and Technology Library

Powered by Koha