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).
Thursdays 3:10pm-4:10pm, Columbine Room 333
Spring 2026 | ||
| Date | Name, Affiliation | Title |
4/2/2026 | Michael Nameika UCCS | Approximating 1D topological insulators in the presence of noisy data |
4/9/2026 | Joseph Noernberg UCCS | Solution dynamics of subcritical NLS systems |
4/16/2026 | Selina Akter UCCS | Rational solutions of the 2D Toda lattice equation |
4/23/2026 | Tori Royall UCCS | The collapsing solutions of the 1D quintic nonlinear Schrödinger equation |
4/24/2026 | Joseph Noernberg UCCS | Dissertation proposal - |
Troy Johnson UCCS | Dissertation proposal - | |
| 4/25/2026 - 4/26/2026 | UCCS | Colorado Nonlinear Days |
Abstracts
Date: April 2, 2026
Speaker: Michael Nameika
Title: Approximating 1D topological insulators in the presence of noisy data
Abstract: We inspect the performance of a nonlinear least squares optimization approach to finding tight-binding coefficients in the Su-Schrieffer-Heeger model for 1D topological insulators when the underlying band or spectral data is corrupted by random, white noise. We show the optimization approach accurately reproduces expected topology and tight binding coefficients of the underlying band or spectral data and converges to the results of the clean model at $\mathcal{O}(N^{-1/2})$ where $N$ is the number of realizations.
Date: April 9, 2026
Speaker: Joseph Noernberg
Title: Solution dynamics of subcritical NLS systems
Abstract: Significant results of the scalar NLS equation are discussed, paving the way for developments of the 1D parity-time NLS system. Consequences of integrability of both systems will be discussed, as well as a result analogous to the virial theorem of the 1D NLS equation. Generic solution dynamics of the 1D parity-time NLS and their apparent relation to the one-soliton breather solution are examined.
Date: April 16, 2026
Speaker: Selina Akter
Title: Rational solutions of the 2D Toda lattice equation
Abstract: The two-dimensional Toda lattice equation is a nonlinear integrable system that exhibits a wide variety of wave phenomena and exact solutions. In this work, a class of rational solutions of the 2D Toda lattice is investigated. These solutions, known as lump solutions, are localized waveforms that decay in all spatial directions and display multi-peak structures.
Date: April 23, 2026
Speaker: Tori Royall
Title: The collapsing solutions of the 1D quintic nonlinear Schrödinger equation
Abstract: An introduction to the 1D Quintic Nonlinear Schrödinger Equation and its collapsing solutions is provided. Methods for numerical simulation and tracking of the position of the closest singularity to the real line are discussed. The approach of collapsing solutions to a self-similar solution is examined. Additionally, dynamic remapping techniques using conformal maps are used to drastically improve the efficiency of the simulation. Finally, the use of fitting techniques to estimate the time of collapse and scalings of the self-similar solution is discussed.
Date: April, 2026
Speaker: Joseph Noernberg
Title: Dissertation proposal -
Abstract:
Date: May, 2026
Speaker: Troy Johnson
Title: Dissertation proposal -
Abstract: