Description
We first explain how the inverse scattering approach to integrable systems can be reformulated in terms of a Riemann–Hilbert problem and then discuss early methods for the solution of such problems using the theory of singular integrals. We then describe the important role played by deformations of a Riemann–Hilbert problem and how this
has led both to detailed information on the long-time asymptotics of integrable PDE and to the incorporation of ever more singular initial data.