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