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 B138
2024-2025 | ||
| Date | Name, Affiliation | Title |
8/24/2024 | Dr. Kenichi Mauruno Waseda University | Delay soliton equations, delay box-ball systems and delay Painlev\'e equations |
2/19/2025 | Dr. Viktor Savchuk Ukraine National Academy of Sciences | Takenaka-Malmquist System and Rational Approximation |
|
|
|
|
|
|
Abstracts
Date: August 24, 2024
Speaker: Kenichi Mauruno
Title: Delay soliton equations, delay box-ball systems and delay Painlev\'e equations
Abstract: We propose a systematic method for constructing integrable delay-difference and delay-differential analogues of known soliton equations such as the Lotka-Volterra and Toda lattice equations and their multi-soliton solutions. Then we construct delay analogues of the box and ball system (BBS) by the ultra-discretization of the delay discrete Lotka-Volterra equation, which is an integrable delay analogue of the discrete Lotka-Volterra equation. Soliton patterns generated by this delay BBS are classified into normal solitons and abnormal solitons. Normal solitons have a clear relationship to the solitons of the BBS with K kinds of balls. On the other hand, abnormal solitons show various types of novel soliton patterns, which have not been observed in almost all known BBSs.
Date: February 19, 2025
Speaker: Viktor Savchuk
Title: Takenaka-Malmquist System and Rational Approximation
Abstract: Functions are fundamental tools for modeling the world around us, but what framework best describes functions themselves? This question is both ambitious and complex. In this talk, I will present results on Fourier series expansions based on the Takenaka-Malmquist (TM) system, a basis of rational functions that plays a crucial role in approximation theory. The key result is that the TM-system provides a “best representation” of functions from the Hardy space, outperforming classical orthonormal bases in certain approximation settings. I will discuss the completeness, optimality, and summability properties of Fourier series based on the TM-system, highlighting its advantages in rational approximation and applications to complex analysis.