• Manuela Girotti
• Assistant Professor
• Emory University
• Date: Sep. 09, Wednesday, 2026
• Time: 14:00-14:50
• Host: Le Chen
• Room: STEM Ag 2111
• Video: Watch this talk on YouTube
• Abstract: The concept of a soliton gas was originally introduced by Zakharov in the Seventies and it can be loosely described as a class of solutions of nonlinear integrable PDEs that displays an infinite number of—possibly random—solitons. I will present a collection of recent results from a collaborative effort to rigorously understand various aspects of several soliton gas models: long-time asymptotics, random statistics, and interaction dynamics. In particular, we consider a gas of random \(N\) solitons for the KdV equation and we study the limit as \(N\) goes to infinity. We derive the limiting solution and we prove that its fluctuations are Gaussian random variables. The starting point is the formulation of a multi-soliton solution and of a regular, dense soliton gas solution in terms of Riemann–Hilbert problems. Tools from asymptotic analysis and probability will be used to provide a detailed description of interesting phenomena.

Recorded for the SASA YouTube channel, with the speaker's consent.