Nonlinear Dirac Equation

DOI10.1090/surv/244zbMath1442.35001OpenAlexW4205692735MaRDI QIDQ5207062

Nabile Boussaid, Andrew Komech

Publication date: 6 January 2020

Published in: Mathematical Surveys and Monographs (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/surv/244

zbMATH Keywords

Schur complementasymptotic stabilityCarleman estimateslimiting absorption principleVakhitov-Kolokolov criterionquintic nonlinearityPokhozhaev identityDerrick theoremDirac-Pauli theoremThiring modelweakly relativistic solitons

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) General topics in linear spectral theory for PDEs (35P05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Bifurcations in context of PDEs (35B32) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41)

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On Solutions with Compact Spectrum to Nonlinear Klein--Gordon and Schrödinger Equations ⋮ An index theorem for one-dimensional gapless non-unitary quantum walks ⋮ Results on the spectral stability of standing wave solutions of the Soler model in 1-D ⋮ Threshold for blowup and stability for nonlinear Schrödinger equation with rotation ⋮ On the nonlinear Dirac equation on noncompact metric graphs ⋮ Nonexistence of self-similar blowup for the nonlinear Dirac equations in \((1+1)\) dimensions ⋮ On asymptotic stability of ground states of some systems of nonlinear Schrödinger equations ⋮ On the one dimensional Dirac equation with potential ⋮ Efficient Scaling and Moving Techniques for Spectral Methods in Unbounded Domains ⋮ The generalized Birman–Schwinger principle ⋮ Limiting absorption principle and virtual levels of operators in Banach spaces

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