Averaging of the nonlinear Schrödinger equation with highly oscillatory magnetic potentials. (June 2017)

• Record Type: Journal Article
• Authors: Feng, Binhua
• Is Part Of: Nonlinear analysis. Volume 156(2017)
• Page Start: 275
• Page End: 285
• Publication Date: 2017-06
• Subjects: Nonlinear Schrödinger equation -- Averaged equation -- Convergence; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.02.028
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study a nonlinear Schrödinger equation with a time-dependent electromagnetic field potential which arises as an effective single particle model in X-ray Free Electron Lasers (XFEL). This equation is the fundamental model in XFEL. We prove the global well-posedness for this equation with an energy subcritical nonlinearity. We extend the study of Antonelli et al. (2014) to power nonlinearity with exponent 4 3 ≤ σ < 4, and our results confirm some numerical results of Huang et al. (2014).