03177nam a22004335i 4500001001800000003000900018005001700027007001500044008004100059020001800100020001900118024003100137082001400168100002600182245016200208264006700370300003200437336002600469337002600495338003600521347002400557490003900581505041100620520122501031650001302256650003402269650002602303650001302329650005702342650003702399650002702436700002602463700002802489710003402517773002002551776003602571830003902607856009702646978-1-4020-3088-8DE-He21320260521092050.0cr nn 008mamaa100301s2005    ne |    s    |||| 0|eng d  a9781402030888  a997814020308887 a10.1007/1-4020-3088-62doi04a530.12231 aGu, Chaohao.eauthor.10aDarboux Transformations in Integrable Systemsh[electronic resource] :bTheory and their Applications to Geometry /cby Chaohao Gu, Hesheng Hu, Zixiang Zhou. 1aDordrecht :bSpringer Netherlands :bImprint: Springer,c2005.  aX, 310 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aMathematical Physics Studies ;v260 a1+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.  aThe 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. 0aPHYSICS. 0aGLOBAL DIFFERENTIAL GEOMETRY. 0aMATHEMATICAL PHYSICS.14aPHYSICS.24aTHEORETICAL, MATHEMATICAL AND COMPUTATIONAL PHYSICS.24aMATHEMATICAL METHODS IN PHYSICS.24aDIFFERENTIAL GEOMETRY.1 aHu, Hesheng.eauthor.1 aZhou, Zixiang.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9781402030871 0aMathematical Physics Studies ;v2640uhttp://dx.doi.org/10.1007/1-4020-3088-6zVer el texto completo en las instalaciones del CICY