Talk by Xi Chen, Part III

This is the Part III/III of the lecture series. This lecture will focus on the explicit formulas initially introduced by Patrick Gérard (2022), a powerful tool that provides more direct access to analyzing the solutions of integrable equations such as the Benjamin-Ono equation and the Calogero-Moser DNLS equation. We will then discuss several applications, including the extension of the flow map, the study of the zerodispersion limit, the characterization of long-time behavior, and the construction of new numerical schemes.