Asymptotic stability of small gap solitons in the nonlinear Dirac\n equations

2010/08/26 by Dmitry E. Pelinovsky, Pelinovsky, Dmitry E., Atanas Stefanov +1 · 5 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Asymptotic analysis #Computer science #Dirac (video compression format) #Dirac equation #Dirac operator #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Nonlinear system #Order (exchange) #Physics #Quantum mechanics #Quintic function #Spectral Theory in Mathematical Physics #Stability (learning theory) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1008.4514

published in arXiv (Cornell University) (Cornell University) · 26 pages, no figures

arxiv created 2010/08/26 · openalex publication_date 2010/08/26 · arxiv updated 2010/08/27 · openalex created_date 2022/10/05 · openalex updated_date 2026/08/08

Abstract

We prove dispersive decay estimates for the one-dimensional Dirac operator\nand use them to prove asymptotic stability of small gap solitons in the\nnonlinear Dirac equations with quintic and higher-order nonlinear terms.\n

Citations

• Time decay for solutions of Schr�dinger equations with rough and time-dependent potentials
• SELECTION OF THE GROUND STATE FOR NONLINEAR SCHRÖDINGER EQUATIONS

Cited by

• Dispersive Estimates for Dirac Operators with General Domain Walls: One and Two Dimensions
• On stability of standing waves of nonlinear Dirac equations
• On the meaning of the Vakhitov-Kolokolov stability criterion for the nonlinear Dirac equation
• Dispersive estimates for Dirac Operators in dimension four with obstructions at threshold energies
• Survey on global existence in the nonlinear Dirac equations in one dimension

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