Mathematics and Statistics Seminar Series
Welcome to the School of Mathematics and Statistics Seminars at RIT. Our events are open to the public, and everyone is welcome to attend.
Join us for our upcoming seminar!
Monday, April 20
2:00 - 2:50 PM
Gleason 1149
Nonlinear waves in two spatial dimensions: Modulation theory, dispersive shocks and applications
Gino Biondini
Darwin D. Martin Professor
Department of Mathematics
State University of New York at Buffalo
Abstract: The talk is aimed at presenting an overview of recent results on the development and application of Whitham modulation theory for two-dimensional nonlinear evolution equations, focusing primarily on the Kadomtsev-Petviashvili (KP) equation. After a brief review of some background material, the first part of the talk will discuss the recently-derived Whitham modulation equations for the KP equation, their properties, and the applications of these modulation equations to characterize (i) the stability of the cnoidal wave solutions of KP, (ii) the temporal evolution of soliton stems, and (iii) the oblique interactions between soliton stems, rarefaction waves (RWs) and dispersive shock waves (DSWs). The second part of the talk will discuss the temporal dynamics generated by wedge-shaped initial conditions in the KP equation. Â Various asymptotic wave patterns are identified, classified and characterized in terms of the incidence angle and the amplitude of the initial step, which can give rise to either subcritical or supercritical configurations, including the generalization to DSWs of the Mach reflection and expansion of viscous shocks and line solitons, and an eightfold amplification of the amplitude of an obliquely incident flow upon a wall at the critical angle. Time permitting, the last part of the talk will discuss the analysis of Riemann problems for the stationary reduction of the KP equation and its application to describe steady shallow water flow past an obstacle, as well as the refraction of line solitons past the resulting RWs and DSWs.
Bio: Gino Biondini received his Ph.D. from the University of Perugia in 1997. After holding post-doctoral positions at University of Colorado, Northwestern University and Ohio State University, in 2004 he joined the Department of Mathematics at the University at Buffalo, State University of New York, where he was promoted to Full Professor in 2011. From 2016 to 2019 he served as Associate Director of the Computational and Data-Enabled Science and Engineering Program, and from 2018 to 2022 he served as Chair of the Department of Mathematics. Prof. Biondini holds two U.S. patents and has published 140 refereed journal articles, which have received over 5600 citations, together with three book chapters and over thirty conference proceedings. He has given over 150 invited presentations at international conferences and academic institutions in the U.S. and abroad. In 2017 he was named an Exceptional Scholar for Sustained Achievement. He has co-edited six special issues of various journals, and in 2023--2024 he served as Chair of the SIAM Activity Group in Nonlinear Waves and Coherent Structures. He is currently serving as editorial board member for Journal of Nonlinear Sciences, Journal of Nonlinear Waves and the East Asian Journal in Applied Mathematics. His main areas of interest include nonlinear wave equations and integrable systems, the inverse scattering transform, solitons, asymptotics and modulation theory, together with their applications to water waves, nonlinear optics, Bose-Einstein condensates and rare event simulation.
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