Singularity Formation in Derivative Nonlinear Schrödinger Equations
Tuesday, November 1, 2016 - 10:15am - 11:05am
Direct numerical simulation of an L2 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. However, 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.