Semiclassical Limit of the Focusing Nonlinear Schrödinger Equation

I will begin by providing some numerical results for the semiclassical limit of the focusing NLS equation. I will then discuss the dispersionless KdV analysis of Lax and Levermore. I will continue by introducing a recent method for solving asymptotic problems for integrable equations (making use of the Riemann-Hilbert factorization formulation of the associated inverse spectral problem). Finally I will apply this method to show how rigorous results for the semiclassical NLS can be obtained.