The 71st Midwest Partial Differential Equations Seminar May 11-12, 2013 Room TBA East Hall University of Michigan Ann Arbor, MI   Abstract Detail   Title: Solitons & Singularities in a Generalized Derivative Nonlinear Schrödinger Equation We examine a generalization of the derivative nonlinear Schrödinger equation, extending it into the L2 supercritical regime. We show that it has solitons and that, depending on the nonlinearity and the soliton parameters, they can be either stable or unstable. Of particular note is that stable solitons are present in the L2 supercritical regime. Furthermore, we find numerical and asymptotic evidence for finite time singularities in the supercritical regime. From our simulations and estimates, we are able to extract both a blowup rate and profile. Open problems and ongoing work will also be discussed. Gideon Simpson University of Minnesota Email:  gsimpson@umn.edu Phone: 2012808006   BACK to Speaker Listing BACK to Conference Home   Sponsors National Science Foundation, Department of Mathematics at the University of Michigan