Abstract

In this talk we will discuss numerical approximations to nonlinear dispersive equations, suited for non-smooth initial data. We will present on the one hand their construction, and on the other hand rigorous low-regularity convergence results in the case of the Gross-Pitaevskii equation.

We will also put forth a novel time discretization to the nonlinear Schrödinger equation, allowing for a low regularity approximation while maintaining good long-time preservation of the mass and energy on the discrete level.

If time permits, higher order extensions will be presented, following new techniques based on decorated trees series expansions inspired by singular stochastic PDEs.