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作者 Boussaid, Nabile, 1978- author
書名 Nonlinear Dirac equation : spectral stability of solitary waves / Nabile Boussaid, Andrew Comech
出版項 Providence, Rhode Island : American Mathematical Society, [2019]
2019
國際標準書號 9781470443955
1470443953
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QC174.45 B7357 2019    在架上    30340200565491
說明 vi, 297 pages : illustrations ; 27 cm
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
系列 Mathematical surveys and monographs, 0076-5376 ; volume 244
Mathematical surveys and monographs ; no. 244. 0076-5376
附註 Includes bibliographical references (pages 279-292) and index
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 Schr诤inger 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
主題 Dirac equation
Wave equation
Differential equations, Partial
Particles (Nuclear physics)
Differential equations, Partial. fast (OCoLC)fst00893484
Dirac equation. fast (OCoLC)fst00894514
Particles (Nuclear physics) fast (OCoLC)fst01054130
Wave equation. fast (OCoLC)fst01172869
Partial differential equations -- Qualitative properties of solutions -- Bifurcation [See also 37Gxx, 37K50]. msc
Partial differential equations -- Qualitative properties of solutions -- Stability. msc
Partial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions. msc
Partial differential equations -- Representations of solutions -- Soliton solutions. msc
Partial differential equations -- Spectral theory and eigenvalue problems [See also 47Axx, 47Bxx, 47F05] -- General topics in linear spectral theory. msc
Partial differential equations -- Spectral theory and eigenvalue problems [See also 47Axx, 47Bxx, 47F05] -- Nonlinear eigenvalue problems, nonlinear spectral theory. msc
Partial differential equations -- Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] -- Time-dependent Schr䁦#x00B6;dinger equations, Dirac equat. msc
Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] -- Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx] -- Soliton theory, asymptotic. msc
Operator theory -- Equations and inequalities involving nonlinear operators [See also 46Txx] {For global and geometric aspects, see 58-XX} -- Nonlinear spectral theory, nonlinear eigenvalue problems [ msc
Quantum theory -- General mathematical topics and methods in quantum theory -- Closed and approximate solutions to the Schr䁦#x00B6;dinger, Dirac, Klein-Gordon and other equations of quantum mechan. msc
Alt Author Komech, Andrew, author
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