Description

Book Synopsis
Presents a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrodinger equation.

Table of Contents
  • Introduction
  • Distributions and function spaces
  • Spectral theory of nonselfadjoint operators
  • Linear stability of NLS solitary waves
  • Solitary waves of nonlinear Schrodinger equation
  • Limiting absorption principle
  • Carleman-Berthier-Georgescu estimates
  • The Dirac matrices
  • The Soler model
  • Bi-frequency solitary waves
  • Bifurcations of eigenvalues from the essential spectrum
  • Nonrelativistic asymptotics of solitary waves
  • Spectral stability in the nonrelativistic limit
  • Bibliography
  • Index
  • List of symbols.

    Nonlinear Dirac Equation Spectral Stability of

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      A Hardback by Nabile Boussaid, Andrew Comech

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        View other formats and editions of Nonlinear Dirac Equation Spectral Stability of by Nabile Boussaid

        Publisher: American Mathematical Society
        Publication Date: Publication Date: 30/01/2020
        ISBN13: 9781470443955, 978-1470443955
        ISBN10: 1470443953

        Description

        Book Synopsis
        Presents a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrodinger equation.

        Table of Contents
        • Introduction
        • Distributions and function spaces
        • Spectral theory of nonselfadjoint operators
        • Linear stability of NLS solitary waves
        • Solitary waves of nonlinear Schrodinger equation
        • Limiting absorption principle
        • Carleman-Berthier-Georgescu estimates
        • The Dirac matrices
        • The Soler model
        • Bi-frequency solitary waves
        • Bifurcations of eigenvalues from the essential spectrum
        • Nonrelativistic asymptotics of solitary waves
        • Spectral stability in the nonrelativistic limit
        • Bibliography
        • Index
        • List of symbols.

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