Modified scattering phenomena of nonlinear dispersive equations

Date
2025/04/11 Fri 16:00 - 17:00
Room
3号館152号室
Speaker
Kiyeon Lee
Affiliation
Korea Advanced Institute of Science and Technology (KAIST)
Abstract

In this talk, we will discuss the modified scattering phenomena of nonlinear dispersive equations. The modified scattering phenomenon is one of the crucial features of dispersive equations in which the dispersive effect is strong. We first introduce the decay properties of some generic dispersive equations to establish the context for scattering results. We also classify the short- and long-range nonlinearities depending on these decay bounds and introduce the asymptotic behavior of long-range nonlinearity, called the modified scattering. Additionally, we describe the space-time resonance method which will play a key role in proving the modified scattering phenomena.