Title: On the Korteweg-de Vries limit for the Fermi-Pasta-Ulam system

Abstract: The Fermi-Pasta-Ulam (FPU) system is a simple nonlinear dynamical lattice model describing a one-dimensional chain of vibrating strings with nearest neighbor interactions. This model was introduced by Fermi, Pasta and Ulam in 1955. It was anticipated at that time that chaotic nonlinear interactions would lead to thermalization. Surprisingly however, numerical simulations showed the opposite behavior -- it exhibited quasi-periodic motions. This phenomenon is known as the FPU paradox. Later, this puzzle has been solved by Zabusky and Kruskal by discovering a formal convergence to the Korteweg-de Vries equation, and the convergence has been rigorously justified. In this talk, we briefly introduce a general approach to prove continuum limit problems using the Fourier transform on a lattice domain. Then, we show that how to put the FPU system into a dispersive PDE framework. This talk is based on joint work with Chulkwang Kwak and Changhun Yang as well as collaboration with Shohei Nakamura and Yukihide Tadano.

About the Speaker: Younghun Hong is in the Department of Mathematics at Chung-Ang University in Seoul, South Korea.  He received his Ph.D. from Brown University in 2013 under the direction of Justin Holmer.  Prior to joining the faculty at Chung-Ang University, he held positions at the University of Texas at Austin and Yonsei University. Professor Hong’s research interests include nonlinear dispersive PDE and harmonic analysis.  Since 2017, his work has been supported by grants through the National Research Foundation of Korea.