Integrable systems applications (42 Ergebnisse)

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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - In this volume nonlinear systems related to integrable systems are studied. Lectures cover such topics as the application of integrable systems to the description of natural phenomena, the elaboration of perturbation theories, and the statistical mechanics of ensembles of objects obeying integrable equations. The more physical lectures center largely around the three paradigmatic equations: Korteweg de Vries, Sine-Gordon and Nonlinear Schrödinger, especially the latter. These have long been of great mathematical interest, and also exhibit a 'universality' which places them among the most frequently encountered integrable equations in the description of physical systems. Tidal waves, optical fibers and laser beams are among the topics discussed. Lectures are also devoted to multidimensional solitons, integrability of Hamiltonian systems of ODEs and dissipative systems of PDEs.…

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Taschenbuch. Zustand: Neu. Darboux Transformations in Integrable Systems | Theory and their Applications to Geometry | Chaohao Gu (u. a.) | Taschenbuch | Mathematical Physics Studies | x | Englisch | 2010 | Springer | EAN 9789048167883 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. …

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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. …

Zustand: New. Based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups. This book contains proofs and explicit calculations, and is useful for graduate students of mathematics. Series: Oxford Lecture Series in Mathematics & Its Applications. Num Pages: 152 pages, Illustrations. BIC Classification: PBKF. Category: (P) Professional & Vocational. Dimension: 249 x 166 x 15. Weight in Grams: 360. . 2005. Illustrated. hardcover. . . . .…

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