Speaker: Chair professor Thanasis Fokas , University of Cambridge

Inviter: Xiang-Ke Chang

Title: Integrable Nonlinear Evolution PDEs: Boundary value Problems and Integrability in three Spatial Dimensions

Language: English

Time & Venue: 2026.06.07 16:00-17:00 南楼N204

Abstract: Following, in the early 1980s, the extension of the Inverse Scattering Method so that it could be applied to integrable nonlinear evolution equations in two special dimensions (like the KP and the DS equations), the most important open problems in the analysis of integrable PDEs became the following: first, solving boundary as opposed to initial value problems and second constructing and solving integrable PDEs in three spatial dimensions. The solutions of these key problems appeared in two publications by the speaker in the Proceedings of the Royal Society in 1997 and 2022 respectively. The former publication gave rise to a new method for solving boundary value problems for linear and for integrable nonlinear PDEs, the so-called Unified Transform (also known as the Fokas method).

For linear PDEs, the relevant transform is based on appropriate deformations of certain integrals from the real line to the complex plane. The idea of deforming to the complex plane has recently led to unexpected and exciting results regarding the large t-asymptotics of the celebrated Riemann zeta function.