03310nam a22004815i 4500 978-1-4020-3088-8 DE-He213 20260521092050.0 cr nn 008mamaa 100301s2005 ne | s |||| 0|eng d 9781402030888 99781402030888 10.1007/1-4020-3088-6 doi 530.1 23 Gu, Chaohao. author. Darboux Transformations in Integrable Systems [electronic resource] : Theory and their Applications to Geometry / by Chaohao Gu, Hesheng Hu, Zixiang Zhou. Dordrecht : Springer Netherlands : Imprint: Springer, 2005. X, 310 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Mathematical Physics Studies ; 26 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. PHYSICS. GLOBAL DIFFERENTIAL GEOMETRY. MATHEMATICAL PHYSICS. PHYSICS. THEORETICAL, MATHEMATICAL AND COMPUTATIONAL PHYSICS. MATHEMATICAL METHODS IN PHYSICS. DIFFERENTIAL GEOMETRY. Hu, Hesheng. author. Zhou, Zixiang. author. SpringerLink (Online service) Springer eBooks Printed edition: 9781402030871 Mathematical Physics Studies ; 26 http://dx.doi.org/10.1007/1-4020-3088-6 Ver el texto completo en las instalaciones del CICY ZDB-2-PHA ddc ER 36264 36264 0 0 ddc 0 0 LE CICY CICY EL 2025-10-06 0 530.1 2025-10-06 08:44:51 2025-10-06 ER