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Backlund Transformations
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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 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 Toda Lattices, Cosymplectic Manifolds, Bäcklund Transformations, and Kinks by : Robert Hermann
Download or read book Toda Lattices, Cosymplectic Manifolds, Bäcklund Transformations, and Kinks written by Robert Hermann and published by Math Science Press. This book was released on 1977 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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.
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 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ba?cklund Transformations and Their Applications
Book Synopsis Introduction to Symmetry Analysis Paperback with CD-ROM by : Brian Cantwell
Download or read book Introduction to Symmetry Analysis Paperback with CD-ROM written by Brian Cantwell and published by Cambridge University Press. This book was released on 2002-09-23 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to symmetry analysis for graduate students in science, engineering and applied mathematics.
Book Synopsis The Geometry of Non-linear Differential Equations, Bäcklund Transformations, and Solitons by : Robert Hermann
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:
Book Synopsis Interdisciplinary Mathematics: The geometry of nonlinear differential equations, Bäcklund transformations, and solitons, pt.A by : Robert Hermann
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 334 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Multidimensional Integrable Equations by : B.G. Konopelchenko
Download or read book Introduction to Multidimensional Integrable Equations written by B.G. Konopelchenko and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Analytical Properties of Nonlinear Partial Differential Equations by : Alexei Cheviakov
Download or read book Analytical Properties of Nonlinear Partial Differential Equations written by Alexei Cheviakov and published by Springer Nature. This book was released on with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integrable Hamiltonian Hierarchies by : Vladimir Gerdjikov
Download or read book Integrable Hamiltonian Hierarchies written by Vladimir Gerdjikov and published by Springer. This book was released on 2008-12-02 with total page 643 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.
Book Synopsis Painlevé Transcendents by : Athanassios S. Fokas
Download or read book Painlevé Transcendents written by Athanassios S. Fokas and published by American Mathematical Society. This book was released on 2023-11-20 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the turn of the twentieth century, the French mathematician Paul Painlevé and his students classified second order nonlinear ordinary differential equations with the property that the location of possible branch points and essential singularities of their solutions does not depend on initial conditions. It turned out that there are only six such equations (up to natural equivalence), which later became known as Painlevé I–VI. Although these equations were initially obtained answering a strictly mathematical question, they appeared later in an astonishing (and growing) range of applications, including, e.g., statistical physics, fluid mechanics, random matrices, and orthogonal polynomials. Actually, it is now becoming clear that the Painlevé transcendents (i.e., the solutions of the Painlevé equations) play the same role in nonlinear mathematical physics that the classical special functions, such as Airy and Bessel functions, play in linear physics. The explicit formulas relating the asymptotic behaviour of the classical special functions at different critical points play a crucial role in the applications of these functions. It is shown in this book that even though the six Painlevé equations are nonlinear, it is still possible, using a new technique called the Riemann-Hilbert formalism, to obtain analogous explicit formulas for the Painlevé transcendents. This striking fact, apparently unknown to Painlevé and his contemporaries, is the key ingredient for the remarkable applicability of these “nonlinear special functions”. The book describes in detail the Riemann-Hilbert method and emphasizes its close connection to classical monodromy theory of linear equations as well as to modern theory of integrable systems. In addition, the book contains an ample collection of material concerning the asymptotics of the Painlevé functions and their various applications, which makes it a good reference source for everyone working in the theory and applications of Painlevé equations and related areas.
Book Synopsis Lie and non-Lie Symmetries: Theory and Applications for Solving Nonlinear Models by : Roman M. Cherniha
Download or read book Lie and non-Lie Symmetries: Theory and Applications for Solving Nonlinear Models written by Roman M. Cherniha and published by MDPI. This book was released on 2018-07-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Lie Theory and Its Applications" that was published in Symmetry
Download or read book Soliton Theory written by Allan P. Fordy and published by Manchester University Press. This book was released on 1990 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent introduction to the complete range of soliton theory including Hirota's method and Backlund transformations. Details physical applications of soliton theory with chapters on the peculiar wave patterns of the Andaman Sea, atmospheric phenomena, general relativity and Davydov solitons. Contains testing for full integrability, a discussion of the Painlevé technique, symmetries and conservation law.
Book Synopsis Geometric Theory of Non-Linear Differential Equations by : Róbert Hermann
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:
Book Synopsis Toda Lattices, Cosymplectic Manifolds, Bäcklund Transformations, and Kinks by : Robert Hermann
Download or read book Toda Lattices, Cosymplectic Manifolds, Bäcklund Transformations, and Kinks written by Robert Hermann and published by . This book was released on 1977 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
