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Dispersive hydrodynamics and Riemann problems in a non-Hermitian, nonlinear Schrödinger equation

Dispersive hydrodynamics and Riemann problems in a non-Hermitian, nonlinear Schrödinger equation

We recently introduced a class of non-centered Riemann problems to an inhomogeneous and non-Hermitian nonlinear Schrödinger equation. The dynamics of these Riemann problems revealed a connection to the wave patterns witnessed in the classical transcritical flow problem. These classical transcritical flow problems were first studied in the context of surface water waves by Grimshaw & Smyth (1986) and in the context of superfluidic condensate flows by Hakim (1997) and more recently Leszczyn et. al. (2009). We point to research directions that are being currently pursued to investigate this connection to classical transcritical flow further.

Brief reviews of the background literature will be part of the talk.

Refreshments will be provided 15 minutes before the event.

## Department of Mathematics and Statistics