Applied Mathematics Seminar-Singularity Formation in Nonlinear Derivative Schrödinger Equations

Title: Singularity Formation in Nonlinear Derivative Schrödinger Equations

Speaker:  Gideon Simpson, Drexel University 

Date and Time:  April 19, 2017, Wednesday,2:30 pm-3:30pm

Place:   Rome 771

Abstract: Direct numerical simulation of an $L^2$ supercritical variant of the derivative nonlinear Schrödinger equation suggests that there is a finite time singularity. Subsequent exploration with the dynamic rescaling method provided more detail about the blowup and a recent refined asymptotic analysis of the blowup solution gives predictions of the blowup rates. Due to the mixed hyperbolic-dispersive nature of the equation, these methods have limited the proximity to the blowup time. Using a locally adaptive meshing method, we are able to overcome these difficulties.