In this talk we will discuss low regularity approximations to nonlinear dispersive equations, both in the case of deterministic and random initial data. We will 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. Higher order extensions will be presented, following new techniques based on decorated trees series analysis inspired by singular SPDEs.
Romain Duboscq, David Lafontaine
