Nonlinear Waves Seminar
Nonlinear Waves
The Nonlinear Waves seminar is motivated by wave phenomena in various systems. However, more broadly, we are interested in computational and applied mathematics. All are welcome to attend. All meetings are in-person, unless specified otherwise.
If you would like to give a talk, email Justin Cole (jcole13@uccs.edu).
Wednesdays, 4:00pm-5:00pm OSB B215
Spring 2023 Abstracts Date: March 22, 2023 Abstract: Dispersive hydrodynamics (DH) is the study of nonlinear dispersive wave dynamics in fluid-like media. A fundamental problem in DH corresponds to studying the dynamics of a Riemann problem: a step-like initial condition connecting two constant amplitude states. Such constant-intensity waves are typically absent in Hermitian, inhomogeneous media, but can exist in non-Hermitian optical media. Thus, we can define and study the notion of non-Hermitian dispersive hydrodynamics and its associated Riemann problems in both ordered and disordered optical media for the first time. These non-Hermitian Riemann problems display rich array of nonlinear wave phenomena due to the loss of space-translational invariance and reflection symmetry. Thus, the location of the initial step is an important parameter, defining the notion of non-centered Riemann problems. For a class of Riemann problems, we point out a connection between the centered and non-centered Riemann problems. Finally, we point to a possible connection with the classical transcritical flow past an obstacle problem (Grimshaw, Smyth 1986) and allude to what could be learnt from here to characterize this present work.
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