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).
Mondays 3:30 pm - 4:30 pm, ACAD 201 (unless colloquium)
Fall 2026 | ||
| Date | Name, Affiliation | Title |
Oct. 16 | Dr. Jianke Yang, Vermont | Wave Patterns in Higher-Order KP-I Lumps (Colloquium) |
Oct. 19 | Dr. Sarbarish Chakravarty, UCCS | Nonstationary Schr\"odinger equation with a special class of rational potentials |
Nov. 2 | Dr. Justin Cole, UCCS | Spiral density waves in disk galaxies |
Dec. 3 | Dr. Ezio Iacocca, UCCS | Artificial Spin Ices (Colloquium) |
Spring 2027 | ||
| Date | Name, Affiliation | Title |
| ||
| ||
| ||
| ||
| ||
| ||
|
| |
Abstracts
Date: Friday October 16
Speaker: Jianke Yang
Title: Wave Patterns in Higher-Order KP-I Lumps (Colloquium)
Abstract: The Kadomtsev-Petviashvili-I (KP-I) equation models two-dimensional shallow water waves under strong surface tension as well as the evolution of weakly nonlinear two-dimensional plasma waves. In this talk, pattern formation in higher-order lumps of the KP-I equation at large times is analytically studied. For these higher-order lumps under certain internal-parameter restrictions, we show that the large-time wave patterns comprise fundamental lumps arranged in non-triangular shapes in the outer region, which are described analytically by nonzero-root structures of the Wronskian-Hermit polynomials, together with fundamental lumps arranged in triangular shapes in the inner region, which are described analytically by root structures of the Yablonskii-Vorob'ev polynomials. When time evolves from large negative to large positive, the non-triangular pattern in the outer region switches its x and y directions, while the triangular pattern in the inner region reverses its direction along the x-axis. For higher-order lumps under generic internal-parameter values, however, we show that the large-time patterns would comprise fundamental lumps in the outer region that are described analytically by the nonzero-root structures of the Wronskian–Hermite polynomials, together with fundamental lumps in the inner region that are uniformly distributed on concentric rings. Our predicted patterns at large times are compared to true solutions, and excellent agreement is observed.
Date: Monday October 19
Speaker: Sarbarish Chakravarty
Title: Nonstationary Schr\"odinger equation with a special class of rational potentials
Abstract: Solutions of the non-stationary Schr\"odinger equation (NSE) associated
with a special class of rational potentials is investigated.
In this particular situation, the potentials satisfy a self-consistency condition
so that the NSE is equivalent to the focusing nonlinear Schr\"odinger equation (NLS)
with non-vanishing boundary conditions. The corresponding NLS solutions are the so
called {\it rogue waves} studied extensively for the past 15
years or so. Furthermore, these NLS--NSE solutions form the eigenfunctions (in Lax
pair sense) of the Kadomtsev-Petviasvili I (KPI) equation, and the associated NSE
potentials (with suitable time-dependence) correspond to a special family of rational,
multi-lump solutions of the KPI equation.
Date: Monday November 2
Speaker: Justin Cole
Title: Spiral density waves in disk galaxies
Abstract: One of the most impressive instances of spiral formation is that of disk galaxies where concentrations of gas induce the creation of new stars in the shape of spirals, including our own Milky Way galaxy. In 1964 Lin and Shu introduced a fluid model to describe galaxy dynamics and the formation of density wave spirals. Therein spiral waves can manifest as linearly unstable perturbations to a radially-symmetric equilibrium solution. This talk will review this problem and discuss new advances to solve it. Numerical results will be presented and compared with empirical findings.
Date: Thursday December 2
Speaker: Ezio Iacocca
Title: Artificial Spin Ices (Colloquium)
Abstract: