中科院数学与系统科学研究院
数学研究所
调和分析及其应用研究中心
学术报告
调和分析和偏微分方程研讨班
报告人：Charles Collot (CY Cergy Paris Université)
题 目：Asymptotic stability of traveling waves for one-dimensional nonlinear Schrodinger equations
时 间：2023.07.11（星期二）16:00-17:00
地 点：数学院南楼N913
摘 要：We consider one dimensional nonlinear Schrodinger equations around a traveling wave. We prove its asymptotic stability for general nonlinearities, under the hypotheses that the orbital stability condition of Grillakis-Shatah-Strauss is satisfied and that the linearized operator does not have a resonance and only has 0 as an eigenvalue. As a by-product of our approach, we show long-range scattering for the radiation remainder. Our proof combines for the first time modulation techniques and the study of space-time resonances. We rely on the use of the distorted Fourier transform, akin to the work of Buslaev and Perelman and, and of Krieger and Schlag, and on precise computations and estimates of space-time resonances to handle its interaction with the soliton. This is joint work with Pierre Germain.
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