This article is concerned with the question of whether it is possible to construct a time
discretization for the one-dimensional cubic nonlinear Schrödinger equation with second …

We introduce a new non-resonant low-regularity integrator for the cubic nonlinear
Schrödinger equation (NLSE) allowing for long-time error estimates which are optimal in the …

We introduce and analyze a symmetric low-regularity scheme for the nonlinear Schrödinger
(NLS) equation beyond classical Fourier-based techniques. We show fractional …

We introduce a unified framework of symmetric resonance based schemes which preserve
central symmetries of the underlying PDE. We extend the resonance decorated trees …

In this paper, we propose a new exponential-type integrator for solving the gKdV equation
under rough data. By introducing new frequency approximation techniques and a key gauge …

In this paper, two semidiscrete low regularity exponential-type integrators are proposed and
analyzed for the “good” Boussinesq equation, including a first-order integrator and a second …

A large toolbox of numerical schemes for dispersive equations has been established, based
on different discretization techniques such as discretizing the variation-of-constants formula …

We propose and analyze a type of low-regularity exponential-type integrators (LREIs) for the
Zakharov system (ZS) with rough solutions. Our LREIs include a first-order integrator and a …

We provide improved uniform error estimates for the time‐splitting Fourier pseudo‐spectral
(TSFP) methods applied to the Klein–Gordon–Dirac system (KGDS) with the small …

We propose and analyze an extended Fourier pseudospectral (eFP) method for the spatial
discretization of the Gross-Pitaevskii equation (GPE) with low regularity potential by treating …