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Author : Irvin W. Kay,Harry E. Moses
Publisher : Math Science Press
Page : 330 pages
File Size : 43,7 Mb
Release : 1982
Category : Mathematics
ISBN : UCAL:B3849278
Author : David H. Sattinger,C. A. Tracy,Stephanos Venakides
Publisher : American Mathematical Soc.
Page : 133 pages
File Size : 41,9 Mb
Release : 1991
Category : Mathematics
ISBN : 9780821851296
This book contains the proceedings of an AMS-IMS-SIAM Summer Institute on Inverse Scattering and Applications, held in Amherst, Massachusetts, in June 1990. The papers cover the current state of the art in inverse conductivity problems, applications of inverse scattering theory to integrable systems, three-dimensional inverse scattering, inverse monodromy problems, and nonlinear waves, among other topics. Intended for researchers working in inverse scattering theory, inverse conductance problems, and completely integrable systems, this book presents results by some of the major experts in the field.
Author : Xudong Chen
Publisher : John Wiley & Sons
Page : 328 pages
File Size : 55,8 Mb
Release : 2018-03-07
Category : Science
ISBN : 9781119312017
A comprehensive and updated overview of the theory, algorithms and applications of for electromagnetic inverse scattering problems Offers the recent and most important advances in inverse scattering grounded in fundamental theory, algorithms and practical engineering applications Covers the latest, most relevant inverse scattering techniques like signal subspace methods, time reversal, linear sampling, qualitative methods, compressive sensing, and noniterative methods Emphasizes theory, mathematical derivation and physical insights of various inverse scattering problems Written by a leading expert in the field
Author : J. Bee Bednar
Publisher : SIAM
Page : 310 pages
File Size : 47,8 Mb
Release : 1983-01-01
Category : Mathematics
ISBN : 0898711908
Author : Peter D. Miller,Peter A. Perry,Jean-Claude Saut,Catherine Sulem
Publisher : Springer Nature
Page : 528 pages
File Size : 45,8 Mb
Release : 2019-11-14
Category : Mathematics
ISBN : 9781493998067
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.
Author : Pham Loi Vu
Publisher : CRC Press
Page : 388 pages
File Size : 55,6 Mb
Release : 2019-11-11
Category : Mathematics
ISBN : 9781000708684
Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations is devoted to inverse scattering problems (ISPs) for differential equations and their application to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, partial differential equations, equations of mathematical physics, and functions of a complex variable. This book is intended for a wide community working with inverse scattering problems and their applications; in particular, there is a traditional community in mathematical physics. In this monograph, the problems are solved step-by-step, and detailed proofs are given for the problems to make the topics more accessible for students who are approaching them for the first time. Features • The unique solvability of ISPs are proved. The scattering data of the considered inverse scattering problems (ISPs) are described completely. • Solving the associated initial value problem or initial-boundary value problem for the nonlinear evolution equations (NLEEs) is carried out step-by-step. Namely, the NLEE can be written as the compatibility condition of two linear equations. The unknown boundary values are calculated with the help of the Lax (generalized) equation, and then the time-dependent scattering data (SD) are constructed from the initial and boundary conditions. • The potentials are recovered uniquely in terms of time-dependent SD, and the solution of the NLEEs is expressed uniquely in terms of the found solutions of the ISP. • Since the considered ISPs are solved well, then the SPs generated by two linear equations constitute the inverse scattering method (ISM). The application of the ISM to solving the NLEEs is consistent and is effectively embedded in the schema of the ISM.
Author : K.I. Hopcraft,P.R. Smith
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 41,7 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401580144
With the advent of the comparatively new disciplines of remote sensing and non-destructive evaluation of materials, the topic of inverse scattering has broadened from its origins in elementary particle physics to encompass a diversity of applications. One such area which is of increasing importance in inverse scattering within the context of electromagnetism and this text aims to serve as an introduction to that particular speciality. The subject's development has progressed at the hands of engineers, mathematicians and physicists alike, with an inevitable disparity of emphasis and notation. One of the main objectives of this text is to distill the essence of the subject and to present it in the form of a graduated and coherent development of ideas and techniques. The text provides a physical approach to inverse scattering solutions, emphasizing the applied aspects rather than the mathematical rigour. The authors' teaching and research backgrounds in physics, electrical engineering and applied mathematics enable them to explore and stress the cross disciplinary nature of the subject. This treatment will be of use to anyone embarking on a theoretical or practical study of inverse electromagnetic scattering.
Author : Vladislav V. Kravchenko
Publisher : Birkhäuser
Page : 154 pages
File Size : 55,8 Mb
Release : 2020-08-18
Category : Mathematics
ISBN : 3030478483
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.
Author : Alexander G. Ramm
Publisher : Springer Nature
Page : 53 pages
File Size : 44,7 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031024184
The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering (;;), where (;;) is the scattering amplitude, ; 2 is the direction of the scattered, incident wave, respectively, 2 is the unit sphere in the R3 and k > 0 is the modulus of the wave vector. The scattering data is called non-over-determined if its dimensionality is the same as the one of the unknown object. By the dimensionality one understands the minimal number of variables of a function describing the data or an object. In an inverse obstacle scattering problem this number is 2, and an example of non-over-determined data is () := (;0;0). By sub-index 0 a fixed value of a variable is denoted. It is proved in this book that the data (), known for all in an open subset of 2, determines uniquely the surface and the boundary condition on . This condition can be the Dirichlet, or the Neumann, or the impedance type. The above uniqueness theorem is of principal importance because the non-over-determined data are the minimal data determining uniquely the unknown . There were no such results in the literature, therefore the need for this book arose. This book contains a self-contained proof of the existence and uniqueness of the scattering solution for rough surfaces.
Author : Robert M. Miura
Publisher : Springer
Page : 302 pages
File Size : 42,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540382201
Proceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974
Author : Daniel Alpay,Bernd Kirstein
Publisher : Birkhäuser
Page : 394 pages
File Size : 52,7 Mb
Release : 2015-04-30
Category : Mathematics
ISBN : 9783319103358
The volume is dedicated to Lev Sakhnovich, who made fundamental contributions in operator theory and related topics. Besides bibliographic material, it includes a number of selected papers related to Lev Sakhnovich's research interests. The papers are related to operator identities, moment problems, random matrices and linear stochastic systems.
Author : R.K. Bullough,P.J. Caudrey
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 54,7 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783642814488
With contributions by numerous experts
Author : Roger G. Newton
Publisher : Springer Science & Business Media
Page : 177 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642836718
Most of the laws of physics are expressed in the form of differential equations; that is our legacy from Isaac Newton. The customary separation of the laws of nature from contingent boundary or initial conditions, which has become part of our physical intuition, is both based on and expressed in the properties of solutions of differential equations. Within these equations we make a further distinction: that between what in mechanics are called the equations of motion on the one hand and the specific forces and shapes on the other. The latter enter as given functions into the former. In most observations and experiments the "equations of motion," i. e. , the structure of the differential equations, are taken for granted and it is the form and the details of the forces that are under investigation. The method by which we learn what the shapes of objects and the forces between them are when they are too small, too large, too remote, or too inaccessi ble for direct experimentation, is to observe their detectable effects. The question then is how to infer these properties from observational data. For the theoreti cal physicist, the calculation of observable consequences from given differential equations with known or assumed forces and shapes or boundary conditions is the standard task of solving a "direct problem. " Comparison of the results with experiments confronts the theoretical predictions with nature.
Author : Z.S. Agranovich,V. A.. Marchenko
Publisher : Courier Dover Publications
Page : 307 pages
File Size : 46,9 Mb
Release : 2020-05-21
Category : Mathematics
ISBN : 9780486842493
This monograph by two Soviet experts in mathematical physics was a major contribution to inverse scattering theory. The two-part treatment examines the boundary-value problem with and without singularities. 1963 edition.
Author : Freeman J. Dyson
Publisher : American Mathematical Soc.
Page : 618 pages
File Size : 54,9 Mb
Release : 1996
Category : Mathematics
ISBN : 0821805614
This book offers a unique compilation of papers in mathematics and physics from Freeman Dyson's 50 years of activity and research. These are the papers that Dyson considers most worthy of preserving, and many of them are classics. The papers are accompanied by commentary explaining the context from which they originated and the subsequent history of the problems that either were solved or left unsolved. This collection offers a connected narrative of the developments in mathematics and physics in which the author was involved, beginning with his professional life as a student of G. H. Hardy.