Nonlinear Waves Seminar

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
Date

Name, University

 Title

January 25

 

 

February 1

 

 

February 8

 Dr. Sarbarish Chakravarty, UCCS

 Rational solutions of KPI equation

February 15

 Cancelled (Snow Day)

 

February 22

  Dr. Sarbarish Chakravarty, UCCS

 Rational solutions of KPI equation (cont.)

March 1

 Dr. Denis Silantyev, UCCS

 Numerical Solutions of gCLM equation with dissipation

March 8

 Dave Milovich, Welkin Sciences in ENG 187

 Unsettled linear algebra of Fourier transforms of complex-coefficient pseudo-Gaussians. 

March 15

 Abdullah Aurko, Florida State University

 (Zoom Talk)

 Instabilities in nonlinear waves using classical and modern      approaches 

March 22

 Sathyanarayanan Chandramouli,

 Florida State University (Zoom Talk)

 Non-Hermitian dispersive hydrodynamics and Riemann problems

March 29

 Spring Break

 

April 5

 Dr. Justin Cole, UCCS  

 Soliton dynamics in the KdV equation with nonzero BCs

April 12

 Dr. Denis Silantyev, UCCS

 Exact Solutions of gCLM equation with dissipation

April 19

 Michael Nameika, UCCS

   

April 26

 Troy Johnson, UCCS

  Numerically approximating rational solutions of PDEs

May 3

 Kyle Rockwell, UCCS

  

Spring 2023 Abstracts

Date:       March 22, 2023
Speaker: Sathyanarayanan Chandramouli
Title: Non-Hermitian dispersive hydrodynamics and Riemann problems

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.