Talk ‘Structure-preserving time integration methods for dispersive wave equations’ at PDETD 2025

I have been invited to give a talk Structure-preserving time integration methods for dispersive wave equations at the workshop Efficient high-order time discretization methods for PDEs in May 2025.

Abstract

Nonlinear dispersive wave equations typically model dispersive effects by third-order spatial or mixed space-time derivatives as in the classical Korteweg-de Vries (KdV) or Benjamin-Bona-Mahony (BBM) equations. Recently, there has been an increasing interest in first-order hyperbolic approximations of these equations, involving some parameters increasing the stiffness of the system in the (formal) limit of the original equations. We present some recent results on structure-preserving discretizations of nonlinear dispersive wave equations, focusing on energy conservation, asymptotic preserving schemes, and efficiency aspects.