Abstract

Dispersive hydrodynamics is an active research area combining mathematical theory and experiments. Most of the research in the area focuses on wave propagation in (a) bulk media, where the governing equations have constant coefficients, or (b) inhomogeneous media, where the underlying dynamical system involves potential terms. In the latter case, the presence of inhomogeneous terms hinders the formulation of a Riemann problem due to the lack of generalized plane wave-type solutions of constant intensity. However, such constant-intensity (CI) solutions in non-Hermitian optical media do exist, allowing us to formulate and study a Riemann problem for the first time therein. After identifying classes of non-Hermitian potentials that support modulationally stable CI states, we motivate the construction of a Riemann problem connecting these CI states. The gain-loss landscape and the loss of symmetries (present in bulk media) lead to rich dispersive hydrodynamic phenomena. My work is a collaborative effort with Nicholas Ossi, Prof. Ziad Musslimani (Florida State University), and Prof. Konstantinos Makris (University of Crete).