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Backlund Transformations And Their Applications
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Book Synopsis Ba?cklund Transformations and Their Applications by : Rogers
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 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ba?cklund Transformations and Their Applications
Book Synopsis Bäcklund Transformations and Their Applications by : C. Rogers
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:
Book Synopsis Lie-Backlund Transformations in Applications by : Robert L. Anderson
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.
Book Synopsis Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications by : Robert M. Miura
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
Book Synopsis Bäcklund and Darboux Transformations by : C. Rogers
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.
Book Synopsis Backlund Transformations, the Inverse Scattering Method, Solitons, and Their Applications by : Robert M. Miura
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:
Book Synopsis Backlund Transformations by : Robert M. Miura
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:
Book Synopsis Lie-Bäcklund Transformations in Applications by : Robert L. Anderson
Download or read book Lie-Bäcklund Transformations in Applications written by Robert L. Anderson and published by . This book was released on 1981 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Local Jet Bundle Formulation of Bäckland Transformations by : F.A.E. Pirani
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.
Book Synopsis Backlund Transformations, the Inverse Scattering Method, Solitons, and Their Applications : Papers by : Robert M. Miura
Download or read book Backlund Transformations, the Inverse Scattering Method, Solitons, and Their Applications : Papers 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:
Book Synopsis Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications by : Robert M. Miura
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:
Book Synopsis Soliton Theory and Its Applications by : Chaohao Gu
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.
Book Synopsis Lie-Bäcklund transformations in applications by : Robert Leonard Anderson
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:
Book Synopsis Backlund Transformations, the Inverse Scattering Method, Solitons, and Their Applications by : Robert M. Miura
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:
Book Synopsis Application of New Bäcklund Transformations for the 2+1 and 3+1 Dimensional Sine-Gordon Equations by : Peter Leth Christiansen
Download or read book Application of New Bäcklund Transformations for the 2+1 and 3+1 Dimensional Sine-Gordon Equations written by Peter Leth Christiansen and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Soliton Theory: Applications to Mechanics by : Ligia Munteanu
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.
Book Synopsis Bäcklund and Darboux Transformations by : A. A. Coley
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.