Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications PDF Download
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Author: Robert M. Miura
Publisher: Springer
ISBN: 3540382208
Category : Mathematics
Languages : en
Pages : 302
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Book Description
Proceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974
Author: Robert M. Miura
Publisher: Springer
ISBN: 3540382208
Category : Mathematics
Languages : en
Pages : 302
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Book Description
Proceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974
Author: Robert L. Anderson
Publisher: SIAM
ISBN: 0898711517
Category : Mathematics
Languages : en
Pages : 131
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Book Description
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: Robert Hermann
Publisher: Math Science Press
ISBN: 9780915692200
Category : Mathematics
Languages : en
Pages : 225
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Book Description
Author: C. Rogers
Publisher: Cambridge University Press
ISBN: 9780521012881
Category : Mathematics
Languages : en
Pages : 436
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Book Description
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: A. A. Coley
Publisher: American Mathematical Soc.
ISBN: 9780821870259
Category : Mathematics
Languages : en
Pages : 460
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Book Description
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: Rogers
Publisher: Academic Press
ISBN: 008095667X
Category : Computers
Languages : en
Pages : 349
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Book Description
Ba?cklund Transformations and Their Applications
Author: Brian Cantwell
Publisher: Cambridge University Press
ISBN: 9780521777407
Category : Mathematics
Languages : en
Pages : 660
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Book Description
An introduction to symmetry analysis for graduate students in science, engineering and applied mathematics.
Author: Victor Daniel Zurkowski
Publisher:
ISBN:
Category :
Languages : en
Pages : 210
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Book Description
Author: Robert Hermann
Publisher:
ISBN:
Category : Ba cklund transformations
Languages : en
Pages : 248
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Book Description
Author: B.G. Konopelchenko
Publisher: Springer Science & Business Media
ISBN: 1489911707
Category : Science
Languages : en
Pages : 298
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Book Description
The soliton represents one ofthe most important ofnonlinear phenomena in modern physics. It constitutes an essentially localizedentity with a set ofremarkable properties. Solitons are found in various areas of physics from gravitation and field theory, plasma physics, and nonlinear optics to solid state physics and hydrodynamics. Nonlinear equations which describe soliton phenomena are ubiquitous. Solitons and the equations which commonly describe them are also of great mathematical interest. Thus, the dis covery in 1967and subsequent development ofthe inversescattering transform method that provides the mathematical structure underlying soliton theory constitutes one of the most important developments in modern theoretical physics. The inversescattering transform method is now established as a very powerful tool in the investigation of nonlinear partial differential equations. The inverse scattering transform method, since its discoverysome two decades ago, has been applied to a great variety of nonlinear equations which arise in diverse fields of physics. These include ordinary differential equations, partial differential equations, integrodifferential, and differential-difference equations. The inverse scattering trans form method has allowed the investigation of these equations in a manner comparable to that of the Fourier method for linear equations.
