Mathematics

Riemann-Hilbert problems provide a powerful analytical tool to study various problems in pure and applied mathematics. In particular, they provide analogues of integral representations for solutions of integrable nonlinear wave equations (e.g. the Korteweg-de Vries equation), from which we can extract detailed information about the wave field with the aid of nonlinear asymptotic analysis methods. In this talk, I will describe the role of Riemann-Hilbert problems in studying solutions of nonlinear wave equations and discuss recent results on so-called rogue waves obtained using this approach.