Rigorous asymptotics of the KdV soliton gas

by Manuela Girotti (Colorado State University)

Location: CYCL02, Louvain-la-Neuve
Time: Tuesday May 29, 2018 at 15:00

We analytically study the long time and large space asymptotics of a KdV soliton gas. A soliton gas can be thought as an infinite collection of interacting solitons randomly distributed on the line. The concept was originally introduced by Zakharov (1971). From a \(2 \times 2\) Riemann-Hilbert problem and via non-linear steepest descent techniques, we are able to extract meaningful information for the solution of the KdV equation in such (random) setting. This is a joint work with Ken McLaughlin (CSU) and Tamara Grava (SISSA).