Scattering And Inverse Scattering On The Line For A First Order System With Energy Dependent Potentials

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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.

Scattering And Inverse Scattering On The Line For A First Order System With Energy Dependent Potentials

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Author : Ramazan Ercan
language : en
Publisher:
Release Date : 2019

Scattering And Inverse Scattering On The Line For A First Order System With Energy Dependent Potentials written by Ramazan Ercan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Differential equations, Linear categories.

A first-order system of two linear ordinary differential equations is analyzed. The linear system contains a spectral parameter, and it has two coefficients that are functions of the spatial variable x. Those two functions act as potentials in the linear system and they also linearly contain the spectral parameter ʎ, and hence they are referred to as energy-dependent potentials. Such a linear system arises in the solution to a pair of integrable nonlinear partial differential equations (known as the derivative nonlinear Schr ̈odinger equations) via the so-called inverse scattering transform method.The direct and inverse problems for the corresponding first-order linear system with energy-dependent potentials are investigated. In the direct problem, when the two potentials belong to the Schwartz class, the properties of the corresponding scattering coefficients and so-called bound-state data are derived. In the inverse problem, the two potentials are recovered from the scattering data set consisting of the scattering coefficients and bound-state data. The solutions to the direct and inverse problems are achieved by relating the scattering data and the potentials in the energy-dependent system to those in a pair of first-order system with energy independent potentials. An alternate solution to the inverse problem is given by formulating a linear integral equation (referred to as the alternate Marchenko integral equation), and the energy-dependent potentials are recovered with the help of the solution to the alternate Marchenko equation.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2005

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

Dissertation Abstracts International

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Author :
language : en
Publisher:
Release Date : 2003

Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Dissertations, Academic categories.

Energy Research Abstracts

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Author :
language : en
Publisher:
Release Date : 1990

Energy Research Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Power resources categories.

Nuclear Science Abstracts

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Author :
language : en
Publisher:
Release Date : 1974-11

Nuclear Science Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-11 with Nuclear energy categories.

Inis Atomindeks

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Author :
language : en
Publisher:
Release Date : 1979

Inis Atomindeks written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Nuclear energy categories.

Encyclopedia Of Nonlinear Science

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Author : Alwyn Scott
language : en
Publisher: Routledge
Release Date : 2006-05-17

Encyclopedia Of Nonlinear Science written by Alwyn Scott and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-17 with Reference categories.

In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.

Physics Briefs

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Author :
language : en
Publisher:
Release Date : 1994

Physics Briefs written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Physics categories.

Fusion Energy Update

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Author :
language : en
Publisher:
Release Date : 1982

Fusion Energy Update written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Controlled fusion categories.