Modified scattering for the one-dimensional cubic nonlinear Schrödinger equation
A talk in the Oberseminar Analysis series by
Jannik Salzwedel
| Abstract: | The one-dimensional cubic nonlinear Schrödinger equation (NLS) is one of the most fundamental models in mathematical physics for describing nonlinear dispersive waves. In this talk, we consider the asymptotic behavior of solutions arising from small and spatially localized initial data. Since the cubic nonlinearity is critical in one dimension, solutions do not scatter to free solutions. Instead, nonlinear effects accumulate over long times and the solutions exhibit modified scattering, a phenomenon that has been studied extensively by a variety of methods. We apply the "testing by wave packets" method of Ifrim and Tataru to the cubic NLS with an additional short-range perturbation, for initial data in the weighted Sobolev space $(H_x^{s,s})$ with $(1/2 < s<1)$, which requires less localization than in previous works. This talk is based on my Master’s thesis written under the guidance of Martin Spitz. Zoom ID: [676 9389 2360] Passcode: [378676 $\href{https://uni-bielefeld.zoom-x.de/j/67693892360?pwd=u5bL8bzpOxFTwMd16V8tZAkB8YAgbv.1 }{\textbf{Join Zoom Meeting}}$ Within the CRC this talk is associated to the project(s): A1 |