Download or read book The Inverse Scattering Transform and the Korteweg de Vries Equation written by Adam Halverson and published by . This book was released on 2000 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book The Inverse Scattering Transformation and The Theory of Solitons written by W. Eckhaus and published by Elsevier. This book was released on 2011-08-18 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Inverse Scattering Transformation and The Theory of Solitons
Download or read book A Perturbation Theory for the Inverse Scattering Transform with Application to the Solution of the Variable Depth Korteweg de Vries Equation written by S. Candler and published by . This book was released on 1985 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse Scattering Method Via the Korteweg De Vries Equation and Its Applications written by Tuyen The Nguyen and published by . This book was released on 1994 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Dispersive Partial Differential Equations and Inverse Scattering written by Peter D. Miller and published by Springer Nature. This book was released on 2019-11-14 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures and invited papers from the Focus Program on "Nonlinear Dispersive Partial Differential Equations and Inverse Scattering" held at the Fields Institute from July 31-August 18, 2017. The conference brought together researchers in completely integrable systems and PDE with the goal of advancing the understanding of qualitative and long-time behavior in dispersive nonlinear equations. The program included Percy Deift’s Coxeter lectures, which appear in this volume together with tutorial lectures given during the first week of the focus program. The research papers collected here include new results on the focusing nonlinear Schrödinger (NLS) equation, the massive Thirring model, and the Benjamin-Bona-Mahoney equation as dispersive PDE in one space dimension, as well as the Kadomtsev-Petviashvili II equation, the Zakharov-Kuznetsov equation, and the Gross-Pitaevskii equation as dispersive PDE in two space dimensions. The Focus Program coincided with the fiftieth anniversary of the discovery by Gardner, Greene, Kruskal and Miura that the Korteweg-de Vries (KdV) equation could be integrated by exploiting a remarkable connection between KdV and the spectral theory of Schrodinger's equation in one space dimension. This led to the discovery of a number of completely integrable models of dispersive wave propagation, including the cubic NLS equation, and the derivative NLS equation in one space dimension and the Davey-Stewartson, Kadomtsev-Petviashvili and Novikov-Veselov equations in two space dimensions. These models have been extensively studied and, in some cases, the inverse scattering theory has been put on rigorous footing. It has been used as a powerful analytical tool to study global well-posedness and elucidate asymptotic behavior of the solutions, including dispersion, soliton resolution, and semiclassical limits.
Download or read book Nonlinear Waves And Inverse Scattering Transform written by Spencer P Kuo and published by World Scientific. This book was released on 2023-06-26 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear waves are essential phenomena in scientific and engineering disciplines. The features of nonlinear waves are usually described by solutions to nonlinear partial differential equations (NLPDEs). This book was prepared to familiarize students with nonlinear waves and methods of solving NLPDEs, which will enable them to expand their studies into related areas. The selection of topics and the focus given to each provide essential materials for a lecturer teaching a nonlinear wave course.Chapter 1 introduces 'mode' types in nonlinear systems as well as Bäcklund transform, an indispensable technique to solve generic NLPDEs for stationary solutions. Chapters 2 and 3 are devoted to the derivation and solution characterization of three generic nonlinear equations: nonlinear Schrödinger equation, Korteweg-de Vries (KdV) equation, and Burgers equation. Chapter 4 is devoted to the inverse scattering transform (IST), addressing the initial value problems of a group of NLPDEs. In Chapter 5, derivations and proofs of the IST formulas are presented. Steps for applying IST to solve NLPDEs for solitary solutions are illustrated in Chapter 6.
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.
Download or read book B cklund 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
Download or read book Asymptotic Analysis of a Class of Perturbed Korteweg de Vries Initial Value Problems written by F. de Kerf and published by . This book was released on 1988 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Peturbation Theory for the Inverse Scattering Transform with Application to the Solution of the Variable Depth Korteweg De Vries Equation written by Stephen Candler and published by . This book was released on 1985 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
Download or read book Direct and Inverse Sturm Liouville Problems written by Vladislav V. Kravchenko and published by Birkhäuser. This book was released on 2020-08-18 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.
Download or read book Hamiltonian Methods in the Theory of Solitons written by Ludwig Faddeev and published by Springer Science & Business Media. This book was released on 2007-08-10 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.
Download or read book Solitons Nonlinear Evolution Equations and Inverse Scattering written by Mark J. Ablowitz and published by Cambridge University Press. This book was released on 1991-12-12 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.
Download or read book Theory of Solitons written by S. Novikov and published by Springer Science & Business Media. This book was released on 1984-05-31 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
