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Author : Rogers
Publisher : Academic Press
ISBN 13 : 008095667X
Total Pages : 333 pages
Book Rating : 4.0/5 (89 download)
Download or read book Ba?cklund Transformations and Their Applications written by Rogers and published by Academic Press. This book was released on 1982-06-18 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ba?cklund Transformations and Their Applications
Author : C. Rogers
Publisher :
ISBN 13 : 9780125928502
Total Pages : 334 pages
Book Rating : 4.9/5 (285 download)
Download or read book Bäcklund Transformations and Their Applications written by C. Rogers and published by . This book was released on 1982 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert M. Miura
Publisher : Springer
ISBN 13 : 3540382208
Total Pages : 302 pages
Book Rating : 4.5/5 (43 download)
Download or read book Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications written by Robert M. Miura and published by Springer. This book was released on 2006-11-14 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974
Author : C. Rogers
Publisher : Cambridge University Press
ISBN 13 : 9780521012881
Total Pages : 436 pages
Book Rating : 4.0/5 (128 download)
Download or read book Bäcklund and Darboux Transformations written by C. Rogers and published by Cambridge University Press. This book was released on 2002-06-24 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the deep and fascinating connections that exist between a ubiquitous class of physically important waves known as solitons and the theory of transformations of a privileged class of surfaces as they were studied by eminent geometers of the nineteenth century. Thus, nonlinear equations governing soliton propagation and also mathematical descriptions of their remarkable interaction properties are shown to arise naturally out of the classical differential geometry of surfaces and what are termed Bäcklund-Darboux transformations.This text, the first of its kind, is written in a straightforward manner and is punctuated by exercises to test the understanding of the reader. It is suitable for use in higher undergraduate or graduate level courses directed at applied mathematicians or mathematical physics.
Author : Robert M. Miura
Publisher :
ISBN 13 : 9783662205938
Total Pages : 308 pages
Book Rating : 4.2/5 (59 download)
Download or read book Backlund Transformations, the Inverse Scattering Method, Solitons, and Their Applications written by Robert M. Miura and published by . This book was released on 2014-01-15 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert L. Anderson
Publisher : SIAM
ISBN 13 : 0898711517
Total Pages : 131 pages
Book Rating : 4.8/5 (987 download)
Download or read book Lie-Backlund Transformations in Applications written by Robert L. Anderson and published by SIAM. This book was released on 1979-06-01 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title presents an introduction to the classical treatment of Backlund and general surface transformations; and includes detailed and accessible techniques for constructing both groups of tranformations which will be of great value to the scientist and engineer in the analysis of mathematical models of physical phenomena. Classical and recent examples of Backlund transformations as applied to geometry, nonlinear optics, turbulence models, nonlinear waves and quantum mechanics are given. The authors discuss applications of Lie-Backlund transformations in mechanics, quantum mechanics, gas dynamics, hydrodynamics, and relativity.
Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (954 download)
Download or read book Backlund Transformations written by and published by . This book was released on 1976 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert M. Miura
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (61 download)
Download or read book Backlund Transformations written by Robert M. Miura and published by . This book was released on 1976 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Chaohao Gu
Publisher : Springer Science & Business Media
ISBN 13 : 3662031027
Total Pages : 414 pages
Book Rating : 4.6/5 (62 download)
Download or read book Soliton Theory and Its Applications written by Chaohao Gu and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Soliton theory is an important branch of applied mathematics and mathematical physics. An active and productive field of research, it has important applications in fluid mechanics, nonlinear optics, classical and quantum fields theories etc. This book presents a broad view of soliton theory. It gives an expository survey of the most basic ideas and methods, such as physical background, inverse scattering, Backlünd transformations, finite-dimensional completely integrable systems, symmetry, Kac-moody algebra, solitons and differential geometry, numerical analysis for nonlinear waves, and gravitational solitons. Besides the essential points of the theory, several applications are sketched and some recent developments, partly by the authors and their collaborators, are presented.
Author : F.A.E. Pirani
Publisher : Springer Science & Business Media
ISBN 13 : 9400995113
Total Pages : 138 pages
Book Rating : 4.4/5 (9 download)
Download or read book Local Jet Bundle Formulation of Bäckland Transformations written by F.A.E. Pirani and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to show that the theory of jet bundles supplies the appropriate setting for the study of Backlund trans formations. These transformations are used to solve certain partial differential equations, particularly non-linear evolution equations. Of course jets have been employed for some time in the theory of partial differential equations, but so far little use has been made of them in applications. In the meanwhile, substantial progress has been made in the study of non-linear evolution equations. This work has been encouraged by the dis covery of remarkable properties of some such equations, for example the existence of soliton solutions and of infinite se quences of conservation laws. Among the techniques devised to deal with these equations are the inverse scattering method and the Backlund transformation. In our opinion the jet bundle formulation offers a unifying geometrical framework for under standing the properties of non-linear evolution equations and the techniques used to deal with them, although we do not consider all of these properties and techniques here. The relevance of the theory of jet bundles lS that it legitimates the practice of regarding the partial derivatives of field variables as independent quantities. Since Backlund trans formations require from the outset manipulation of these partial derivatives, and repeated shifts of point of view about which variables are dependent on which, this geometrical setting clari fies and simplifies the concepts involved, and offers the prospect of bringing coherence to a variety of disparate results.
Author : Chaohao Gu
Publisher : Springer Science & Business Media
ISBN 13 : 1402030886
Total Pages : 308 pages
Book Rating : 4.4/5 (2 download)
Download or read book Darboux Transformations in Integrable Systems written by Chaohao Gu and published by Springer Science & Business Media. This book was released on 2006-07-09 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Ligia Munteanu
Publisher : Springer Science & Business Media
ISBN 13 : 9781402025761
Total Pages : 338 pages
Book Rating : 4.0/5 (257 download)
Download or read book Introduction to Soliton Theory: Applications to Mechanics written by Ligia Munteanu and published by Springer Science & Business Media. This book was released on 2004-08-11 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is planned to provide the application of the soliton theory to solve certain practical problems selected from the fields of solid mechanics, fluid mechanics and biomechanics. The work is based mainly on the authors’ research carried out at their home institutes, and on some specified, significant results existing in the published literature. The methodology to study a given evolution equation is to seek the waves of permanent form, to test whether it possesses any symmetry properties, and whether it is stable and solitonic in nature. Students of physics, applied mathematics, and engineering are usually exposed to various branches of nonlinear mechanics, especially to the soliton theory. The soliton is regarded as an entity, a quasi-particle, which conserves its character and interacts with the surroundings and other solitons as a particle. It is related to a strange phenomenon, which consists in the propagation of certain waves without attenuation in dissipative media. This phenomenon has been known for about 200 years (it was described, for example, by the Joule Verne's novel Les histoires de Jean Marie Cabidoulin, Éd. Hetzel), but its detailed quantitative description became possible only in the last 30 years due to the exceptional development of computers. The discovery of the physical soliton is attributed to John Scott Russell. In 1834, Russell was observing a boat being drawn along a narrow channel by a pair of horses.
Author : Robert M. Miura
Publisher :
ISBN 13 :
Total Pages : 295 pages
Book Rating : 4.:/5 (476 download)
Download or read book Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications written by Robert M. Miura and published by . This book was released on 1976 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. A. Coley
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870259
Total Pages : 460 pages
Book Rating : 4.8/5 (72 download)
Download or read book Bäcklund and Darboux Transformations written by A. A. Coley and published by American Mathematical Soc.. This book was released on 2001-01-01 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a classical topic that has undergone rapid and fruitful development over the past 25 years, namely Backlund and Darboux transformations and their applications in the theory of integrable systems, also known as soliton theory. The book consists of two parts. The first is a series of introductory pedagogical lectures presented by leading experts in the field. They are devoted respectively to Backlund transformations of Painleve equations, to the dressing methodand Backlund and Darboux transformations, and to the classical geometry of Backlund transformations and their applications to soliton theory. The second part contains original contributions that represent new developments in the theory and applications of these transformations. Both the introductorylectures and the original talks were presented at an International Workshop that took place in Halifax, Nova Scotia (Canada). This volume covers virtually all recent developments in the theory and applications of Backlund and Darboux transformations.
Author : Robert M. Miura
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (93 download)
Download or read book Backlund Transformations, the Inverse Scattering Method, Solitons, and Their Applications written by Robert M. Miura and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert Leonard Anderson
Publisher :
ISBN 13 :
Total Pages : 124 pages
Book Rating : 4.:/5 (878 download)
Download or read book Lie-Bäcklund transformations in applications written by Robert Leonard Anderson and published by . This book was released on 1979 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : E. Atlee Jackson
Publisher : CUP Archive
ISBN 13 : 9780521426336
Total Pages : 676 pages
Book Rating : 4.4/5 (263 download)
Download or read book Perspectives of Nonlinear Dynamics: Volume 2 written by E. Atlee Jackson and published by CUP Archive. This book was released on 1989 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dynamics of physical, chemical, biological or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations.
