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Author : Robert Hermann
Publisher :
ISBN 13 :
Total Pages : 316 pages
Book Rating : 4.F/5 ( download)
Download or read book The Geometry of Non-linear Differential Equations, Bäcklund Transformations, and Solitons written by Robert Hermann and published by . This book was released on 1976 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert Hermann
Publisher :
ISBN 13 :
Total Pages : 338 pages
Book Rating : 4.3/5 (91 download)
Download or read book Interdisciplinary Mathematics: The geometry of nonlinear differential equations, Bäcklund transformations, and solitons, pt.A written by Robert Hermann and published by . This book was released on 1973 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert Hermann
Publisher :
ISBN 13 :
Total Pages : 358 pages
Book Rating : 4.3/5 (91 download)
Download or read book Interdisciplinary Mathematics: The geometry of nonlinear differential equations, Bäcklund fransformations, and solitons, pt.B written by Robert Hermann and published by . This book was released on 1973 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : P.A. Clarkson
Publisher : Springer Science & Business Media
ISBN 13 : 940112082X
Total Pages : 466 pages
Book Rating : 4.4/5 (11 download)
Download or read book Applications of Analytic and Geometric Methods to Nonlinear Differential Equations written by P.A. Clarkson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton' equations. (2) Twistor theory, using differential geometry, which has been used to solve the self-dual Yang--Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied. Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations; subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. `soliton' systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations. (ABSTRACT) In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for `soliton' equations and twistor theory, for the self-dual Yang--Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations.
Author : Ivan V Cherednik
Publisher : World Scientific
ISBN 13 : 9814499005
Total Pages : 264 pages
Book Rating : 4.8/5 (144 download)
Download or read book Basic Methods Of Soliton Theory written by Ivan V Cherednik and published by World Scientific. This book was released on 1996-08-22 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 25 years of its existence Soliton Theory has drastically expanded our understanding of “integrability” and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.Differential algebra (local conservation laws, Bäcklund-Darboux transforms), algebraic geometry (theta and Baker functions), and the inverse scattering method (Riemann-Hilbert problem) with well-grounded preliminaries are applied to various equations including principal chiral fields, Heisenberg magnets, Sin-Gordon, and Nonlinear Schrödinger equation.
Author : Robert Hermann
Publisher :
ISBN 13 : 9780915692293
Total Pages : 610 pages
Book Rating : 4.6/5 (922 download)
Download or read book Cartanian Geometry, Nonlinear Waves, and Control Theory written by Robert Hermann and published by . This book was released on 1979 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert Hermann
Publisher : Math Science Press
ISBN 13 :
Total Pages : 360 pages
Book Rating : 4.:/5 (318 download)
Download or read book The Geometry of Non-linear Differential Equations, Bäcklund Transformations, and Solitons written by Robert Hermann and published by Math Science Press. This book was released on 1977 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alex Kasman
Publisher : American Mathematical Soc.
ISBN 13 : 0821852450
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)
Download or read book Glimpses of Soliton Theory written by Alex Kasman and published by American Mathematical Soc.. This book was released on 2010 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. --
Author : Robert L. Anderson
Publisher : Siam
ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.F/5 ( 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 with total page 144 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 : F. Calogero
Publisher : Elsevier
ISBN 13 : 9780080875347
Total Pages : 515 pages
Book Rating : 4.8/5 (753 download)
Download or read book Spectral Transform and Solitons written by F. Calogero and published by Elsevier. This book was released on 2011-08-18 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Transform and Solitons
Author : Stig Lundqvist
Publisher : Springer Science & Business Media
ISBN 13 : 1489920587
Total Pages : 482 pages
Book Rating : 4.4/5 (899 download)
Download or read book Order and Chaos in Nonlinear Physical Systems written by Stig Lundqvist and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is concerned with the theoretical description of patterns and instabilities and their relevance to physics, chemistry, and biology. More specifically, the theme of the work is the theory of nonlinear physical systems with emphasis on the mechanisms leading to the appearance of regular patterns of ordered behavior and chaotic patterns of stochastic behavior. The aim is to present basic concepts and current problems from a variety of points of view. In spite of the emphasis on concepts, some effort has been made to bring together experimental observations and theoretical mechanisms to provide a basic understanding of the aspects of the behavior of nonlinear systems which have a measure of generality. Chaos theory has become a real challenge to physicists with very different interests and also in many other disciplines, of which astronomy, chemistry, medicine, meteorology, economics, and social theory are already embraced at the time of writing. The study of chaos-related phenomena has a truly interdisciplinary charac ter and makes use of important concepts and methods from other disciplines. As one important example, for the description of chaotic structures the branch of mathematics called fractal geometry (associated particularly with the name of Mandelbrot) has proved invaluable. For the discussion of the richness of ordered structures which appear, one relies on the theory of pattern recognition. It is relevant to mention that, to date, computer studies have greatly aided the analysis of theoretical models describing chaos.
Author : R. Martini
Publisher : Springer
ISBN 13 : 354038166X
Total Pages : 350 pages
Book Rating : 4.5/5 (43 download)
Download or read book Geometrical Approaches to Differential Equations written by R. Martini and published by Springer. This book was released on 2006-11-15 with total page 350 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 : Karl Lanngren
Publisher : Elsevier
ISBN 13 : 0323156444
Total Pages : 315 pages
Book Rating : 4.3/5 (231 download)
Download or read book Solutions In Action written by Karl Lanngren and published by Elsevier. This book was released on 2012-12-02 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solitons in Action is a collection of papers that discusses the concept of a wave packer or pulse known as a soliton. One paper reviews the development of the solitary wave concept, with emphasis on the difference between a solitary wave and a soliton. The Korteweg-deVries (KdV) equation shows the interactions between infinite sets of conservation laws and the inverse scattering transform method. The Backlund transform technique produces hierarchies of multisoliton solutions for nonlinear wave equations. The Gel-'fand-Levitan algorithm can effect an inverse scattering calculation that relates changes in the scattering data to changes in the solution of corresponding wave equation. One paper points out that concepts in differential geometry can show the fundamental nature of soliton behavior and the relationship between inverse scattering and the Backlund transformation. Solitons in action can be viewed as magnetic flux propagates through a gap (between two closely-spaced superconductors) in quantum units. This view results in a simplified procedure for perturbation expansions around multisoliton solutions. This collection can prove useful for researchers involved in the study of fluid mechanics, of pure and applied sciences, of mathematical sciences, and of wave theory.
Author : Lokenath Debnath
Publisher : Springer Science & Business Media
ISBN 13 : 0817644180
Total Pages : 738 pages
Book Rating : 4.8/5 (176 download)
Download or read book Nonlinear Partial Differential Equations for Scientists and Engineers written by Lokenath Debnath and published by Springer Science & Business Media. This book was released on 2010-02-20 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expanded, revised edition is a thorough and systematic treatment of linear and nonlinear partial differential equations and their varied applications. It contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, make the book useful for a diverse readership including graduates, researchers, and professionals in mathematics, physics and engineering.
Author : Róbert Hermann
Publisher :
ISBN 13 : 9780915692163
Total Pages : 313 pages
Book Rating : 4.6/5 (921 download)
Download or read book Geometric Theory of Non-Linear Differential Equations written by Róbert Hermann and published by . This book was released on 1977 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt:
