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4:00 pm Wednesday, September 10, 2008 Geometry-Analysis Seminar: Breaking in the Semiclassical Solution of the Focusing Nonlinear Schrödinger Equationby Sergey Belov (Rice University) in HB 227- We study the one dimensional semiclassical focusing cubic nonlinear Schrödinger equation with a one parameter family of decaying initial conditions using the Lax pair and the Riemann-Hilbert approach to inverse scattering. In previous studies the solution was found to develop fast oscillations in modulus passed some curves in the space-time plane (breaking curves or nonlinear caustics). We will carry out an asymptotic analysis of the solution as we approach a catastrophic break of the our analytic procedure. We will also talk about numerical integration on a Riemann surface to compute the relevant quantities numerically near the catastrophic break and providing new insights to the first break.
Submitted by damanik@rice.edu |