Semiclassical limit of nonlinear Schrödinger and Davey-Stewartson equations
Seminar Room 1, Newton Institute
The semiclassical limit of nonlinear Schrödinger and Davey-Stewartson equations is a small dispersion limit of purely dispersive PDEs. In the vicinity of shocks of the corresponding dispersionless equations, the solutions develop a zone of rapid modulated oscillations. The case of the focusing equations is especially interesting since the dispersionless equations as well as Whitham's averaged equations are elliptic. We present an asymptotic description of the breakup in the 1-dimensional case and a numerical study of the higher dimensional cases.