Direct And Inverse Scattering For The Matrix Schr Dinger Equation
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Direct And Inverse Scattering For The Matrix Schr Dinger Equation
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Author : Tuncay Aktosun
language : en
Publisher: Springer Nature
Release Date : 2020-05-19
Direct And Inverse Scattering For The Matrix Schr Dinger Equation written by Tuncay Aktosun and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-19 with Mathematics categories.
Authored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schrödinger equation on the half line with the general selfadjoint boundary condition. The existence, uniqueness, construction, and characterization aspects are treated with mathematical rigor, and physical insight is provided to make the material accessible to mathematicians, physicists, engineers, and applied scientists with an interest in scattering and inverse scattering. The material presented is expected to be useful to beginners as well as experts in the field. The subject matter covered is expected to be interesting to a wide range of researchers including those working in quantum graphs and scattering on graphs. The theory presented is illustrated with various explicit examples to improve the understanding of scattering and inverse scattering problems. The monograph introduces a specific class of input data sets consisting of a potential and a boundary condition and a specific class of scattering data sets consisting of a scattering matrix and bound-state information. The important problem of the characterization is solved by establishing a one-to-one correspondence between the two aforementioned classes. The characterization result is formulated in various equivalent forms, providing insight and allowing a comparison of different techniques used to solve the inverse scattering problem. The past literature treated the type of boundary condition as a part of the scattering data used as input to recover the potential. This monograph provides a proper formulation of the inverse scattering problem where the type of boundary condition is no longer a part of the scattering data set, but rather both the potential and the type of boundary condition are recovered from the scattering data set.
Direct And Inverse Scattering For The Matrix Schr Dinger Equation
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Author : Tuncay Aktosun
language : en
Publisher:
Release Date : 2021
Direct And Inverse Scattering For The Matrix Schr Dinger Equation written by Tuncay Aktosun and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Scattering (Mathematics) categories.
Authored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schrödinger equation on the half line with the general selfadjoint boundary condition. The existence, uniqueness, construction, and characterization aspects are treated with mathematical rigor, and physical insight is provided to make the material accessible to mathematicians, physicists, engineers, and applied scientists with an interest in scattering and inverse scattering. The material presented is expected to be useful to beginners as well as experts in the field. The subject matter covered is expected to be interesting to a wide range of researchers including those working in quantum graphs and scattering on graphs. The theory presented is illustrated with various explicit examples to improve the understanding of scattering and inverse scattering problems. The monograph introduces a specific class of input data sets consisting of a potential and a boundary condition and a specific class of scattering data sets consisting of a scattering matrix and bound-state information. The important problem of the characterization is solved by establishing a one-to-one correspondence between the two aforementioned classes. The characterization result is formulated in various equivalent forms, providing insight and allowing a comparison of different techniques used to solve the inverse scattering problem. The past literature treated the type of boundary condition as a part of the scattering data used as input to recover the potential. This monograph provides a proper formulation of the inverse scattering problem where the type of boundary condition is no longer a part of the scattering data set, but rather both the potential and the type of boundary condition are recovered from the scattering data set.
Boundary Value Problems Integral Equations And Related Problems Proceedings Of The International Conference
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Author : Guo Chun Wen
language : en
Publisher: World Scientific
Release Date : 2000-02-22
Boundary Value Problems Integral Equations And Related Problems Proceedings Of The International Conference written by Guo Chun Wen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-22 with Science categories.
In this proceedings volume, the following topics are discussed: (1) various boundary value problems for partial differential equations and functional equations, including free and moving boundary problems; (2) the theory and methods of integral equations and integral operators, including singular integral equations; (3) applications of boundary value problems and integral equations to mechanics and physics; (4) numerical methods of integral equations and boundary value problems; and (5) some problems related with analysis and the foregoing subjects.
Solitons Nonlinear Evolution Equations And Inverse Scattering
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Author : Mark J. Ablowitz
language : en
Publisher: Cambridge University Press
Release Date : 1991-12-12
Solitons Nonlinear Evolution Equations And Inverse Scattering written by Mark J. Ablowitz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-12-12 with Mathematics categories.
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.
Inverse Scattering Problems And Their Application To Nonlinear Integrable Equations
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Author : Pham Loi Vu
language : en
Publisher: CRC Press
Release Date : 2023-05-15
Inverse Scattering Problems And Their Application To Nonlinear Integrable Equations written by Pham Loi Vu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-15 with Mathematics categories.
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.
An Introduction To Inverse Problems In Physics
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Author : Mohsen Razavy
language : en
Publisher: World Scientific
Release Date : 2020-05-21
An Introduction To Inverse Problems In Physics written by Mohsen Razavy and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-21 with Science categories.
This book is a compilation of different methods of formulating and solving inverse problems in physics from classical mechanics to the potentials and nucleus-nucleus scattering. Mathematical proofs are omitted since excellent monographs already exist dealing with these aspects of the inverse problems.The emphasis here is on finding numerical solutions to complicated equations. A detailed discussion is presented on the use of continued fractional expansion, its power and its limitation as applied to various physical problems. In particular, the inverse problem for discrete form of the wave equation is given a detailed exposition and applied to atomic and nuclear scattering, in the latter for elastic as well as inelastic collision. This technique is also used for inverse problem of geomagnetic induction and one-dimensional electrical conductivity. Among other topics covered are the inverse problem of torsional vibration, and also a chapter on the determination of the motion of a body with reflecting surface from its reflection coefficient.
Scattering Two Volume Set
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Author : E. R. Pike
language : en
Publisher: Academic Press
Release Date : 2002
Scattering Two Volume Set written by E. R. Pike and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Science categories.
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.
On The Direct And Inverse Scattering For The Matrix Schroedinger Equation On The Line
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Author : University of Minnesota. Institute for Mathematics and Its Applications
language : en
Publisher:
Release Date : 1999
On The Direct And Inverse Scattering For The Matrix Schroedinger Equation On The Line written by University of Minnesota. Institute for Mathematics and Its Applications and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Spectral Geometry Of Graphs
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Author : Pavel Kurasov
language : en
Publisher: Springer Nature
Release Date : 2023-11-07
Spectral Geometry Of Graphs written by Pavel Kurasov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-07 with Science categories.
This open access book gives a systematic introduction into the spectral theory of differential operators on metric graphs. Main focus is on the fundamental relations between the spectrum and the geometry of the underlying graph. The book has two central themes: the trace formula and inverse problems. The trace formula is relating the spectrum to the set of periodic orbits and is comparable to the celebrated Selberg and Chazarain-Duistermaat-Guillemin-Melrose trace formulas. Unexpectedly this formula allows one to construct non-trivial crystalline measures and Fourier quasicrystals solving one of the long-standing problems in Fourier analysis. The remarkable story of this mathematical odyssey is presented in the first part of the book. To solve the inverse problem for Schrödinger operators on metric graphs the magnetic boundary control method is introduced. Spectral data depending on the magnetic flux allow one to solve the inverse problem in full generality, this means to reconstruct not only the potential on a given graph, but also the underlying graph itself and the vertex conditions. The book provides an excellent example of recent studies where the interplay between different fields like operator theory, algebraic geometry and number theory, leads to unexpected and sound mathematical results. The book is thought as a graduate course book where every chapter is suitable for a separate lecture and includes problems for home studies. Numerous illuminating examples make it easier to understand new concepts and develop the necessary intuition for further studies.
Scattering And Biomedical Engineering
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Author : Christos Massalas
language : en
Publisher: World Scientific
Release Date : 2002
Scattering And Biomedical Engineering written by Christos Massalas and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Medical categories.
This volume deals with scattering theory, applied mathematics, modeling and biomedical engineering. Most of the papers describe mathematical methods, numerical solutions and models for well-known problems in those areas.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)