Inverse Scattering And Applications

Author : David H. Sattinger,C. A. Tracy,Stephanos Venakides
Publisher : American Mathematical Soc.
Page : 133 pages
File Size : 51,8 Mb
Release : 1991
Category : Mathematics
ISBN : 9780821851296

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Inverse Scattering and Applications by David H. Sattinger,C. A. Tracy,Stephanos Venakides Pdf

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 : Pham Loi Vu
Publisher : CRC Press
Page : 453 pages
File Size : 54,6 Mb
Release : 2023-05-15
Category : Mathematics
ISBN : 9781000872057

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Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations by Pham Loi Vu Pdf

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.

Author : J. Bee Bednar
Publisher : SIAM
Page : 310 pages
File Size : 54,8 Mb
Release : 1983-01-01
Category : Mathematics
ISBN : 0898711908

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Conference on Inverse Scattering--Theory and Application by J. Bee Bednar Pdf

Author : Anonim
Publisher : Unknown
Page : 133 pages
File Size : 40,6 Mb
Release : 1991
Category : Inverse problems (Differential equations)
ISBN : LCCN:91026094

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Inverse Scattering and Applications by Anonim Pdf

Author : Pham Loi Vu
Publisher : CRC Press
Page : 388 pages
File Size : 43,9 Mb
Release : 2019-11-11
Category : Mathematics
ISBN : 9781000708684

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Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations by Pham Loi Vu Pdf

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 : Robert M. Miura
Publisher : Springer
Page : 302 pages
File Size : 47,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540382201

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Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications by Robert M. Miura Pdf

Proceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974

Author : Khosrow Chadan,David Colton,Lassi P?iv?rinta,William Rundell
Publisher : SIAM
Page : 206 pages
File Size : 45,6 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 9780898713879

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An Introduction to Inverse Scattering and Inverse Spectral Problems by Khosrow Chadan,David Colton,Lassi P?iv?rinta,William Rundell Pdf

Here is a clearly written introduction to three central areas of inverse problems: inverse problems in electromagnetic scattering theory, inverse spectral theory, and inverse problems in quantum scattering theory. Inverse problems, one of the most attractive parts of applied mathematics, attempt to obtain information about structures by nondestructive measurements. Based on a series of lectures presented by three of the authors, all experts in the field, the book provides a quick and easy way for readers to become familiar with the area through a survey of recent developments in inverse spectral and inverse scattering problems.

Author : Fioralba Cakoni,David Colton,Houssem Haddar
Publisher : SIAM
Page : 203 pages
File Size : 54,7 Mb
Release : 2016-10-28
Category : Mathematics
ISBN : 9781611974461

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Inverse Scattering Theory and Transmission Eigenvalues by Fioralba Cakoni,David Colton,Houssem Haddar Pdf

Inverse scattering theory is a major theme of applied mathematics, and it has applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting particular problems in the development of efficient inversion algorithms. Although linearized models continue to play an important role in many applications, an increased need to focus on problems in which multiple scattering effects cannot be ignored has led to a central role for nonlinearity, and the possibility of collecting large amounts of data over limited regions of space means that the ill-posed nature of the inverse scattering problem has become a problem of central importance.? Initial efforts to address the nonlinear and the ill-posed nature of the inverse scattering problem focused on nonlinear optimization methods. While efficient in many situations, strong a priori information is necessary for their implementation. This problem led to a qualitative approach to inverse scattering theory in which the amount of a priori information is drastically reduced, although at the expense of only obtaining limited information about the values of the constitutive parameters. This qualitative approach (the linear sampling method, the factorization method, the theory of transmission eigenvalues, etc.) is the theme of Inverse Scattering Theory and Transmission Eigenvalues.? The authors begin with a basic introduction to the theory, then proceed to more recent developments, including a detailed discussion of the transmission eigenvalue problem; present the new generalized linear sampling method in addition to the well-known linear sampling and factorization methods; and in order to achieve clarification of presentation, focus on the inverse scattering problem for scalar homogeneous media.?

Author : J. L. Bona,Roy Choudhury,David Kaup,Ams-IMS-Siam Joint Summer Research Conference on the Legacy of Inverse Scattering Transfor
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 40,5 Mb
Release : 2002
Category : Science
ISBN : 9780821831618

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The Legacy of the Inverse Scattering Transform in Applied Mathematics by J. L. Bona,Roy Choudhury,David Kaup,Ams-IMS-Siam Joint Summer Research Conference on the Legacy of Inverse Scattering Transfor Pdf

Swift progress and new applications characterize the area of solitons and the inverse scattering transform. There are rapid developments in current nonlinear optical technology: Larger intensities are more available; pulse widths are smaller; relaxation times and damping rates are less significant. In keeping with these advancements, exactly integrable soliton equations, such as $3$-wave resonant interactions and second harmonic generation, are becoming more and more relevant in experimental applications. Techniques are now being developed for using these interactions to frequency convert high intensity sources into frequency regimes where there are no lasers. Other experiments involve using these interactions to develop intense variable frequency sources, opening up even more possibilities. This volume contains new developments and state-of-the-art research arising from the conference on the ""Legacy of the Inverse Scattering Transform"" held at Mount Holyoke College (South Hadley, MA). Unique to this volume is the opening section, ""Reviews"". This part of the book provides reviews of major research results in the inverse scattering transform (IST), on the application of IST to classical problems in differential geometry, on algebraic and analytic aspects of soliton-type equations, on a new method for studying boundary value problems for integrable partial differential equations (PDEs) in two dimensions, on chaos in PDEs, on advances in multi-soliton complexes, and on a unified approach to integrable systems via Painleve analysis. This conference provided a forum for general exposition and discussion of recent developments in nonlinear waves and related areas with potential applications to other fields. The book will be of interest to graduate students and researchers interested in mathematics, physics, and engineering.

Author : K.I. Hopcraft,P.R. Smith
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 52,5 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401580144

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An Introduction to Electromagnetic Inverse Scattering by K.I. Hopcraft,P.R. Smith Pdf

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 : Mark J. Ablowitz,Harvey Segur
Publisher : SIAM
Page : 433 pages
File Size : 49,5 Mb
Release : 2006-05-15
Category : Mathematics
ISBN : 9780898714777

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Solitons and the Inverse Scattering Transform by Mark J. Ablowitz,Harvey Segur Pdf

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.

Author : Fioralba Cakoni,David Colton,Houssem Haddar
Publisher : SIAM
Page : 200 pages
File Size : 44,6 Mb
Release : 2016-10-28
Category : Mathematics
ISBN : 9781611974454

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Inverse Scattering Theory and Transmission Eigenvalues by Fioralba Cakoni,David Colton,Houssem Haddar Pdf

Inverse scattering theory is a major theme of applied mathematics, and it has applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting particular problems in the development of efficient inversion algorithms. Although linearized models continue to play an important role in many applications, an increased need to focus on problems in which multiple scattering effects cannot be ignored has led to a central role for nonlinearity, and the possibility of collecting large amounts of data over limited regions of space means that the ill-posed nature of the inverse scattering problem has become a problem of central importance. Initial efforts to address the nonlinear and the ill-posed nature of the inverse scattering problem focused on nonlinear optimization methods. While efficient in many situations, strong a priori information is necessary for their implementation. This problem led to a qualitative approach to inverse scattering theory in which the amount of a priori information is drastically reduced, although at the expense of only obtaining limited information about the values of the constitutive parameters. This qualitative approach (the linear sampling method, the factorization method, the theory of transmission eigenvalues, etc.) is the theme of Inverse Scattering Theory and Transmission Eigenvalues. The authors begin with a basic introduction to the theory, then proceed to more recent developments, including a detailed discussion of the transmission eigenvalue problem; present the new generalized linear sampling method in addition to the well-known linear sampling and factorization methods; and in order to achieve clarification of presentation, focus on the inverse scattering problem for scalar homogeneous media.

Author : Vladislav V. Kravchenko
Publisher : Birkhäuser
Page : 154 pages
File Size : 54,7 Mb
Release : 2020-08-18
Category : Mathematics
ISBN : 3030478483

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Direct and Inverse Sturm-Liouville Problems by Vladislav V. Kravchenko Pdf

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 : E. R. Pike,Pierre C. Sabatier
Publisher : Academic Press
Page : 985 pages
File Size : 40,7 Mb
Release : 2002
Category : Science
ISBN : 9780126137606

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Scattering, Two-Volume Set by E. R. Pike,Pierre C. Sabatier Pdf

Part 1: SCATTERING OF WAVES BY MACROSCOPIC TARGET -- Interdisciplinary aspects of wave scattering -- Acoustic scattering -- Acoustic scattering: approximate methods -- Electromagnetic wave scattering: theory -- Electromagnetic wave scattering: approximate and numerical methods -- Electromagnetic wave scattering: applications -- Elastodynamic wave scattering: theory -- Elastodynamic wave scattering: Applications -- Scattering in Oceans -- Part 2: SCATTERING IN MICROSCOPIC PHYSICS AND CHEMICAL PHYSICS -- Introduction to direct potential scattering -- Introduction to Inverse Potential Scattering -- Visible and Near-visible Light Scattering -- Practical Aspects of Visible and Near-visible Light Scattering -- Nonlinear Light Scattering -- Atomic and Molecular Scattering: Introduction to Scattering in Chemical -- X-ray Scattering -- Neutron Scattering -- Electron Diffraction and Scattering -- Part 3: SCATTERING IN NUCLEAR PHYSICS -- Nuclear Physics -- Part 4: PARTICLE SCATTERING -- State of the Art of Peturbative Methods -- Scattering Through Electro-weak Interactions (the Fermi Scale) -- Scattering Through Strong Interactions (the Hadronic or QCD Scale) -- Part 5: SCATTERING AT EXTREME PHYSICAL SCALES -- Scattering at Extreme Physical Scales -- Part 6: SCATTERING IN MATHEMATICS AND NON-PHYSICAL SCIENCES -- Relations with Other Mathematical Theories -- Inverse Scattering Transform and Non-linear Partial Differenttial Equations -- Scattering of Mathematical Objects.

Author : Robert M. Miura
Publisher : Unknown
Page : 308 pages
File Size : 51,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662205939

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Backlund Transformations, the Inverse Scattering Method, Solitons, and Their Applications by Robert M. Miura Pdf