Solitons and channels of energy for nonlinear waves
Organizers
Speaker
Carlos Kenig
Time
Wednesday, September 10, 2025 5:00 PM - 6:30 PM
Venue
A6-101
Online
Zoom 388 528 9728
(BIMSA)
Abstract
We will recall the origins of Fourier analysis and its connection to partial differential equations through the work of Fourier on heat conduction in the early 19’th century. This led to the representation of solutions of evolutionary equations by the Fourier method, as a superposition of plane waves, a remarkable “simplification” that transformed the study of linear partial differential equations and led to fundamental technical advances in the 19th century. With the advent of computers in the middle of the 20’th century, through the remarkable computations of Fermi-‐Pasta-‐Ulam (mid50s) and Kruskal-‐Zabusky (mid 60s) it was observed numerically that nonlinear equations modeling wave propagation, asymptotically, also exhibit a “simplification”, this time as superposition of “traveling waves” and “radiation”. This has become known as the “soliton resolution conjecture”. The only proofs available have been for “integrable” equations, which can be reduced to a collection of linear equations. The proof of such results, in the non-‐integrable case, has been one of the grand challenges in the study of nonlinear differential equations. Recently, there have been important breakthroughs in obtaining mathematical proofs of these types of numerical observations, in the context of nonlinear wave equations, which I will discuss.
Speaker Intro
Carlos Eduardo Kenig is a Louis Block Distinguished Service Professor in the Department of Mathematics at the University of Chicago. He is known for his work in harmonic analysis and partial differential equations. He was an invited speaker at ICM2002 and a plenary speaker at ICM2010. He is a member of the American Academy of Arts and Sciences since 2002, and the National Academy of Sciences since 2014. He was president of the International Mathematical Union between 2019 and 2022.