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Nonlinear Dirac Equation: Spectral Stability of Solitary Waves, Nabile Boussaid, Andrew Comech


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Автор: Nabile Boussaid, Andrew Comech
Название:  Nonlinear Dirac Equation: Spectral Stability of Solitary Waves
ISBN: 9781470443955
Издательство: Mare Nostrum (Eurospan)
Классификация:
ISBN-10: 1470443953
Обложка/Формат: Hardback
Страницы: 297
Вес: 0.74 кг.
Дата издания: 30.01.2020
Серия: Mathematical surveys and monographs
Язык: English
Размер: 186 x 262 x 23
Ключевые слова: Calculus & mathematical analysis,Differential calculus & equations
Подзаголовок: Spectral stability of solitary waves
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Поставляется из: Англии
Описание: 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 available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves.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. It also presents the necessary tools such as the limiting absorption principle and the Carleman estimates in the form applicable to the Dirac operator, and proves the general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation.
Дополнительное описание: Differential calculus and equations|Calculus and mathematical analysis



The Many Faces of Maxwell, Dirac and Einstein Equations

Автор: Waldyr A. Rodrigues; Edmundo C. Oliveira
Название: The Many Faces of Maxwell, Dirac and Einstein Equations
ISBN: 3642090389 ISBN-13(EAN): 9783642090387
Издательство: Springer
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Цена: 16070.00 р.
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Описание: This book is a comprehensive reference on differential geometry. It shows that Maxwell, Dirac and Einstein fields, which were originally considered objects of a very different mathematical nature, have representatives as objects of the same mathematical nature. The book also analyzes some foundational issues of relativistic field theories.

Spectral and Dynamical Stability of Nonlinear Waves

Автор: Todd Kapitula; Keith Promislow
Название: Spectral and Dynamical Stability of Nonlinear Waves
ISBN: 1461469945 ISBN-13(EAN): 9781461469940
Издательство: Springer
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Цена: 11878.00 р.
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Описание: This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes the fundamental ideas of the past two decades of research, carefully balancing theory and application.

Spectral and Dynamical Stability of Nonlinear Waves

Автор: Todd Kapitula; Keith Promislow
Название: Spectral and Dynamical Stability of Nonlinear Waves
ISBN: 1493901877 ISBN-13(EAN): 9781493901876
Издательство: Springer
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Цена: 8384.00 р.
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Описание: This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes the fundamental ideas of the past two decades of research, carefully balancing theory and application.

The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator

Автор: J.J. Duistermaat
Название: The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator
ISBN: 1461253462 ISBN-13(EAN): 9781461253464
Издательство: Springer
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Цена: 11173.00 р.
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Описание: for two weeks in October 1994, Victor Guillemin made me enthusiastic about a problem in symplectic geometry which involved the use of the so-called spin-c Dirac operator. I thank the Editorial Board of Birkhauser, especially Haim Brezis, for sug- gesting the publication of these notes as a book.

Sturm—Liouville and Dirac Operators

Автор: Levitan; I.S. Sargsjan
Название: Sturm—Liouville and Dirac Operators
ISBN: 0792309928 ISBN-13(EAN): 9780792309925
Издательство: Springer
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Цена: 15372.00 р.
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Описание: 'Et moi, ...- si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point allC: .' human. race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'ttre of this series.

The Dirac Spectrum

Автор: Nicolas Ginoux
Название: The Dirac Spectrum
ISBN: 3642015697 ISBN-13(EAN): 9783642015694
Издательство: Springer
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Цена: 5583.00 р.
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Описание: Surveys the spectral properties of the spin Dirac operator. Introducing spin geometry, this title presents the main known estimates for Dirac eigenvalues on compact manifolds with or without boundaries. It gives examples where the spectrum can be made explicit and also presents a chapter dealing with the non-compact setting.

Dirac Kets, Gamow Vectors and Gel`fand Triplets

Автор: Arno Bohm; Arno Bohm; J.D. Dollard; Manuel Gadella
Название: Dirac Kets, Gamow Vectors and Gel`fand Triplets
ISBN: 3662137518 ISBN-13(EAN): 9783662137512
Издательство: Springer
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Цена: 11753.00 р.
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Описание: The results are then deepened by giving the analytic tools, such as the Hardy class function and Hilbert and Mellin transforms, needed in applications to physical problems. Applications are given to physical theories of such phenomena as decaying states and resonances.

Analysis of Dirac Systems and Computational Algebra

Автор: Fabrizio Colombo; Irene Sabadini; Franciscus Somme
Название: Analysis of Dirac Systems and Computational Algebra
ISBN: 1461264693 ISBN-13(EAN): 9781461264699
Издательство: Springer
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Цена: 6986.00 р.
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Описание:

* The main treatment is devoted to the analysis of systems of linear partial differential equations (PDEs) with constant coefficients, focusing attention on null solutions of Dirac systems

* All the necessary classical material is initially presented

* Geared toward graduate students and researchers in (hyper)complex analysis, Clifford analysis, systems of PDEs with constant coefficients, and mathematical physics


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