题目: Asymptotic stability of traveling waves for one-dimensional nonlinear Schrodinger equations

报告人：Charles Collot (CY Cergy Paris Université)

时间：5月5日16:00-17:00

地点：Zoom meeting

https://nus-sg.zoom.us/j/81029937256?pwd=4fzMYehUQejXoj6x7bkJxwOdb55Vn5.1

Meeting ID: 810 2993 7256

Passcode: 683388

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 renormalizations, computations and estimates of space-time resonances to handle its interaction with the soliton. This is joint work with Pierre Germain.