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Inverse Problems and Nonlinear Evolution Equations : Solutions, Darboux Matrices and Weyl–Titchmarsh Functions

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Title: Inverse Problems and Nonlinear Evolution Equations : Solutions, Darboux Matrices and Weyl–Titchmarsh Functions
Description: This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund–Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.
Authors: Alexander L. Sakhnovich, Lev A. Sakhnovich, Inna Ya. Roitberg
Resource Type: eBook.
Subjects: Matrices, Boundary value problems, Darboux transformations, Functions, Evolution equations, Nonlinear, Inverse problems (Differential equations)
Categories: MATHEMATICS / Differential Equations / General, SCIENCE / Physics / Mathematical & Computational
Database: eBook Collection (EBSCOhost)
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DbLabel: eBook Collection (EBSCOhost)
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PubType: eBook
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  Data: Inverse Problems and Nonlinear Evolution Equations : Solutions, Darboux Matrices and Weyl–Titchmarsh Functions
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  Data: This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund–Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.
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  Data: <searchLink fieldCode="AR" term="%22Alexander+L%2E+Sakhnovich%22">Alexander L. Sakhnovich</searchLink><br /><searchLink fieldCode="AR" term="%22Lev+A%2E+Sakhnovich%22">Lev A. Sakhnovich</searchLink><br /><searchLink fieldCode="AR" term="%22Inna+Ya%2E+Roitberg%22">Inna Ya. Roitberg</searchLink>
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  Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Differential+Equations+%2F+General%22">MATHEMATICS / Differential Equations / General</searchLink><br /><searchLink fieldCode="ZK" term="%22SCIENCE+%2F+Physics+%2F+Mathematical+%26+Computational%22">SCIENCE / Physics / Mathematical & Computational</searchLink>
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RecordInfo BibRecord:
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      – Code: 515.357
        Scheme: ddc
        Type: prePub
      – Code: 515.357
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Matrices
        Type: general
      – SubjectFull: Boundary value problems
        Type: general
      – SubjectFull: Darboux transformations
        Type: general
      – SubjectFull: Functions
        Type: general
      – SubjectFull: Evolution equations, Nonlinear
        Type: general
      – SubjectFull: Inverse problems (Differential equations)
        Type: general
    Titles:
      – TitleFull: Inverse Problems and Nonlinear Evolution Equations : Solutions, Darboux Matrices and Weyl–Titchmarsh Functions
        Type: main
  BibRelationships:
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      – PersonEntity:
          Name:
            NameFull: Alexander L. Sakhnovich
      – PersonEntity:
          Name:
            NameFull: Lev A. Sakhnovich
      – PersonEntity:
          Name:
            NameFull: Inna Ya. Roitberg
      – PersonEntity:
          Name:
            NameFull: Alexander L. Sakhnovich
      – PersonEntity:
          Name:
            NameFull: Lev A. Sakhnovich
      – PersonEntity:
          Name:
            NameFull: Inna Ya. Roitberg
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2013
            – D: 04
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9783110258608
            – Type: isbn-electronic
              Value: 9783110258615
          Titles:
            – TitleFull: Inverse Problems and Nonlinear Evolution Equations : Solutions, Darboux Matrices and Weyl–Titchmarsh Functions
              Type: main
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