Speaker
Description
Based on a joint work with Mattia Cafasso and Tom Claeys, we consider a novel class of solutions to the Korteweg-de Vries (KdV) equation, defined for t>0 and blowing up at t=0; they arise in connection with a multiplicative statistics of the Airy point process. Such class can be regarded as a broad generalization of the classical self-similar KdV solution associated with the Ablowitz-Segur Painlevé II (PII) transcendents. In general, these solutions are instead connected with an integro-differential deformation of the PII equation; this deformation has been first found by Amir, Corwin, and Quastel in their study of the KPZ stochastic PDE with narrow wedge initial conditions. We provide a Riemann-Hilbert (RH) approach to these solutions, and thus the study of their initial value problem is amenable by the Deift-Zhou asymptotic analysis of the RH problem.
