Integrable Systems and Random Matrix Theory Seminar

We will discuss the long-time asymptotic behavior of oscillatory Riemann-Hilbert problems (RHPs) arising in the mKdV hierarchy (reducing from the AKNS hierarchy). Our analysis is based on the idea of dbar-steepest descent. We will consider RHPs generated from the inverse scattering transform of the AKNS hierarchy with weighted Sobolev initial data. The asymptotic formula for three regions (Oscillating, fast decaying, Painleve region) of the spatial and temporal dependent variables will be presented. Speaker(s): Fudong Wang (University of Central Florida)