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Darboux Transformations in Integrable Systems

Theory and their Applications to Geometry

This book is available for download with iBooks on your Mac or iOS device, and with iTunes on your computer. Books can be read with iBooks on your Mac or iOS device.

Description

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.

Darboux Transformations in Integrable Systems
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  • 129,99 €
  • Available on iPhone, iPad, iPod touch, and Mac.
  • Category: Science & Nature
  • Published: 09 July 2006
  • Publisher: Springer Netherlands
  • Print Length: 318 Pages
  • Language: English
  • Requirements: To view this book, you must have an iOS device with iBooks 1.3.1 or later and iOS 4.3.3 or later, or a Mac with iBooks 1.0 or later and OS X 10.9 or later.

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