Sathya Chandramouli, Department of Mathematics and Statistics, University of Massachusetts Amherst

Transcritical flow problem in the nonlinear Schrödinger equation with Wadati potential

A past work led to the identification of a class of Riemann problems to a transformed nonlinear Schrödinger equation with complex Wadati potential. Here, features reminiscent of the classical transcritical flow (resonant generation of dispersive shock waves) problem (Grimshaw and Smyth, '86), (Leszczyszyn et.al., '09) were observed.  The present work defines and substantiates the optical flow over a Wadati "obstacle". Here, the difference between earlier studies on the transcritical condensate flow over a penetrable barrier (Leszczyszyn et.al., '09) correspond to an attractive (or focusing) optical barrier (potential), and crucially, the presence of an externally imposed gain-loss landscape. An appropriate scaling symmetry defines a three-parameter family of optical flow problems. We classify and study these flow patterns with a combination of numerical simulations and hydraulic theory. This is joint work with Prof. Mark Hoefer and Dr. Patrick Sprenger.