The recipient of the Gårding prize in 2025, Jonatan Lenells, will give a talk about his research aimed towards a broad audience. Eva and Lars Gårding’s prize, administered by the Royal Physiographic Society of Lund, is intended for the promotion of research and for rewarding scientific excellence in the fields of Mathematics and Linguistics. It is awarded for Mathematics during odd years and for Linguistics during even years.

Title: Soliton equations

Abstract:

I will give an overview of mathematical tools developed over the past half century for the study of a class of nonlinear partial differential equations known as soliton equations. In particular, I will describe how these tools can be used to obtain remarkably precise asymptotic formulas for the solution. The theory will be illustrated with the help of two celebrated equations for water waves: the Korteweg–de Vries equation and the Boussinesq equation.