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Backland Transformations The Inverse Scattering Method Solitions And Their Applications
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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 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 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 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 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 Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications by : Martin L. Silverstein
Download or read book Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications written by Martin L. Silverstein and published by . This book was released on 1976 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations by : Pham Loi Vu
Download or read book Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations written by Pham Loi Vu and published by CRC Press. This book was released on 2023-05-15 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Scattering Problems and Their Applications to Nonlinear Integrable Equations, Second Edition is devoted to inverse scattering problems (ISPs) for differential equations and their applications to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, differential equations, and equations of mathematical physics. This book is intended for a wide community working with ISPs and their applications. There is an especially strong traditional community in mathematical physics. In this monograph, the problems are presented step-by-step, and detailed proofs are given for considered problems to make the topics more accessible for students who are approaching them for the first time. New to the Second Edition All new chapter dealing with the Bäcklund transformations between a common solution of both linear equations in the Lax pair and the solution of the associated IBVP for NLEEs on the half-line Updated references and concluding remarks Features Solving the direct and ISP, then solving the associated initial value problem (IVP) or initial-boundary value problem (IBVP) for NLEEs are carried out step-by-step. The unknown boundary values are calculated with the help of the Lax (generalized) equations, then the time-dependent scattering data (SD) are expressed in terms of preassigned initial and boundary conditions. Thereby, the potential functions are recovered uniquely in terms of the given initial and calculated boundary conditions. The unique solvability of the ISP is proved and the SD of the scattering problem is described completely. The considered ISPs are well-solved. The ISPs are set up appropriately for constructing the Bӓckhund transformations (BTs) for solutions of associated IBVPs or IVPs for NLEEs. The procedure for finding a BT for the IBVP for NLEEs on the half-line differs from the one used for obtaining a BT for non-linear differential equations defined in the whole space. The interrelations between the ISPs and the constructed BTs are established to become new powerful unified transformations (UTs) for solving IBVPs or IVPs for NLEEs, that can be used in different areas of physics and mechanics. The application of the UTs is consistent and efficiently embedded in the scheme of the associated ISP.
Book Synopsis BACKLUND TRANSFORMATIONS, THE INVERSE SCATTERING METHOD, SOLITONS AND THEIR APPLICATIONS- PAPERS PRESENTED AT A NSF RESEARCH WORKSHOP ON CONTACT TRANSFORMATIONS- NATIONAL SCIENCE FOUNDATION. by : NATIONAL SCIENCE FOUNDATION.
Download or read book BACKLUND TRANSFORMATIONS, THE INVERSE SCATTERING METHOD, SOLITONS AND THEIR APPLICATIONS- PAPERS PRESENTED AT A NSF RESEARCH WORKSHOP ON CONTACT TRANSFORMATIONS- NATIONAL SCIENCE FOUNDATION. written by NATIONAL SCIENCE FOUNDATION. and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Solitons and the Inverse Scattering Transform by : Mark J. Ablowitz
Download or read book Solitons and the Inverse Scattering Transform written by Mark J. Ablowitz and published by SIAM. This book was released on 2006-05-15 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.
Book Synopsis Bäcklund Transformations, the Inverse Scattering Method, Solitons and Their Applications. NSF Research Workshop on Contact Transformations. Vanderbilt University in Nashville, Tennessee. 27-29 September, 1974 by : Robert M. Miura
Download or read book Bäcklund Transformations, the Inverse Scattering Method, Solitons and Their Applications. NSF Research Workshop on Contact Transformations. Vanderbilt University in Nashville, Tennessee. 27-29 September, 1974 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 Direct and Inverse Scattering on the Line by : Richard Beals
Download or read book Direct and Inverse Scattering on the Line written by Richard Beals and published by American Mathematical Soc.. This book was released on 2015-03-02 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the theory of linear ordinary differential operators of arbitrary order. Unlike treatments that focus on spectral theory, this work centers on the construction of special eigenfunctions (generalized Jost solutions) and on the inverse problem: the problem of reconstructing the operator from minimal data associated to the special eigenfunctions. In the second order case this program includes spectral theory and is equivalent to quantum mechanical scattering theory; the essential analysis involves only the bounded eigenfunctions. For higher order operators, bounded eigenfunctions are again sufficient for spectral theory and quantum scattering theory, but they are far from sufficient for a successful inverse theory. The authors give a complete and self-contained theory of the inverse problem for an ordinary differential operator of any order. The theory provides a linearization for the associated nonlinear evolution equations, including KdV and Boussinesq. The authors also discuss Darboux-Bäcklund transformations, related first-order systems and their evolutions, and applications to spectral theory and quantum mechanical scattering theory. Among the book's most significant contributions are a new construction of normalized eigenfunctions and the first complete treatment of the self-adjoint inverse problem in order greater than two. In addition, the authors present the first analytic treatment of the corresponding flows, including a detailed description of the phase space for Boussinesq and other equations. The book is intended for mathematicians, physicists, and engineers in the area of soliton equations, as well as those interested in the analytical aspects of inverse scattering or in the general theory of linear ordinary differential operators. This book is likely to be a valuable resource to many. Required background consists of a basic knowledge of complex variable theory, the theory of ordinary differential equations, linear algebra, and functional analysis. The authors have attempted to make the book sufficiently complete and self-contained to make it accessible to a graduate student having no prior knowledge of scattering or inverse scattering theory. The book may therefore be suitable for a graduate textbook or as background reading in a seminar.
Book Synopsis Perspectives of Nonlinear Dynamics: Volume 1 by : E. Atlee Jackson
Download or read book Perspectives of Nonlinear Dynamics: Volume 1 written by E. Atlee Jackson and published by CUP Archive. This book was released on 1989 with total page 532 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. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.
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 Inverse Scattering and Applications by : David H. Sattinger
Download or read book Inverse Scattering and Applications written by David H. Sattinger and published by American Mathematical Soc.. This book was released on 1991 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents papers given at a Conference on Inverse Scattering on the Line, held in June 1990 at the University of Massachusetts, Amherst. A wide variety of topics in inverse problems were covered: inverse scattering problems on the line; inverse problems in higher dimensions; inverse conductivity problems; and numerical methods. In addition, problems from statistical physics were covered, including monodromy problems, quantum inverse scattering, and the Bethe ansatz. One of the aims of the conference was to bring together researchers in a variety of areas of inverse problems which have seen intensive activity in recent years. scattering
Book Synopsis The Painlevé Handbook by : Robert M. Conte
Download or read book The Painlevé Handbook written by Robert M. Conte and published by Springer Science & Business Media. This book was released on 2008-11-23 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear differential or difference equations are encountered not only in mathematics, but also in many areas of physics (evolution equations, propagation of a signal in an optical fiber), chemistry (reaction-diffusion systems), and biology (competition of species). This book introduces the reader to methods allowing one to build explicit solutions to these equations. A prerequisite task is to investigate whether the chances of success are high or low, and this can be achieved without any a priori knowledge of the solutions, with a powerful algorithm presented in detail called the Painlevé test. If the equation under study passes the Painlevé test, the equation is presumed integrable. If on the contrary the test fails, the system is nonintegrable or even chaotic, but it may still be possible to find solutions. The examples chosen to illustrate these methods are mostly taken from physics. These include on the integrable side the nonlinear Schrödinger equation (continuous and discrete), the Korteweg-de Vries equation, the Hénon-Heiles Hamiltonians, on the nonintegrable side the complex Ginzburg-Landau equation (encountered in optical fibers, turbulence, etc), the Kuramoto-Sivashinsky equation (phase turbulence), the Kolmogorov-Petrovski-Piskunov equation (KPP, a reaction-diffusion model), the Lorenz model of atmospheric circulation and the Bianchi IX cosmological model. Written at a graduate level, the book contains tutorial text as well as detailed examples and the state of the art on some current research.
Book Synopsis Methods of Inverse Problems in Physics by : Dilip N. Ghosh Roy
Download or read book Methods of Inverse Problems in Physics written by Dilip N. Ghosh Roy and published by CRC Press. This book was released on 1991-03-14 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This interesting volume focuses on the second of the two broad categories into which problems of physical sciences fall-direct (or forward) and inverse (or backward) problems. It emphasizes one-dimensional problems because of their mathematical clarity. The unique feature of the monograph is its rigorous presentation of inverse problems (from quantum scattering to vibrational systems), transmission lines, and imaging sciences in a single volume. It includes exhaustive discussions on spectral function, inverse scattering integral equations of Gel'fand-Levitan and Marcenko, Povzner-Levitan and Levin transforms, Møller wave operators and Krein's functionals, S-matrix and scattering data, and inverse scattering transform for solving nonlinear evolution equations via inverse solving of a linear, isospectral Schrodinger equation and multisoliton solutions of the K-dV equation, which are of special interest to quantum physicists and mathematicians. The book also gives an exhaustive account of inverse problems in discrete systems, including inverting a Jacobi and a Toeplitz matrix, which can be applied to geophysics, electrical engineering, applied mechanics, and mathematics. A rigorous inverse problem for a continuous transmission line developed by Brown and Wilcox is included. The book concludes with inverse problems in integral geometry, specifically Radon's transform and its inversion, which is of particular interest to imaging scientists. This fascinating volume will interest anyone involved with quantum scattering, theoretical physics, linear and nonlinear optics, geosciences, mechanical, biomedical, and electrical engineering, and imaging research.
