Nonlinear Partial Differential Equations

Date: April 12, 2022

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Gong Chen, University of Kentucky

Title: Long-time dynamics of 1d cubic nonlinear Schrödinger equations with a trapping potential

Abstract: We will consider the long-time dynamics of small solutions to the 1d cubic nonlinear Schrödinger equation (NLS) with a trapping potential. I will illustrate that every small solution will decompose into a small solitary wave and a radiation term which exhibits the modified scattering. The analysis also establishes the long-time behavior of solutions to a perturbation of the integrable cubic NLS with the appearance of solitons.