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Nonlinear Dirac equation : spectral stability of solitary waves

Author: Nabile Boussaïd; Andrew Komech
Publisher: Providence, Rhode Island : American Mathematical Society, [2019] ©2019
Series: Mathematical surveys and monographs, 244
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Boussaïd, Nabile, 1978-
Nonlinear Dirac equation.
Providence, Rhode Island : American Mathematical Society, [2019]
(DLC) 2019029167
(OCoLC)1124776702
Material Type: Document
Document Type: Book, Computer File
All Authors / Contributors: Nabile Boussaïd; Andrew Komech
ISBN: 9781470454227 147045422X
OCLC Number: 1130766963
Description: 1 online resource (vi, 297 pages) : illustrations
Contents: Distributions and function spaces --
Spectral theory of nonselfadjoint operators --
Linear stability of NLS solitary waves --
Solitary waves of nonlinear Schrödinger 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 nonrelativistics limit
Series Title: Mathematical surveys and monographs, 244
Responsibility: Nabile Boussaïd, Andrew Comech

Abstract:

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  Read more...

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