A fully discrete and fully explicit low-regularity integrator is constructed for the one-
dimensional periodic cubic nonlinear Schrödinger equation. The method can be …

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 …

In this paper, we introduce a novel class of embedded exponential-type low-regularity
integrators (ELRIs) for solving the KdV equation and establish their optimal convergence …

In this paper, we propose a first-order Fourier integrator for solving the cubic nonlinear
Schrödinger equation in one dimension. The scheme is explicit and can be implemented …

In this paper, we propose an embedded low-regularity integrator (ELRI) under a new
framework for solving the modified Korteweg-de Vries (mKdV) equation under rough data …

In this paper, we establish the optimal convergence for a second-order exponential-type
integrator from Hofmanová & Schratz (2017, An exponential-type integrator for the KdV …

This article is concerned with the construction and analysis of new time discretizations for
the KdV equation on a torus for low-regularity solutions below $ H^ 1$. New harmonic …

A new harmonic analysis technique by using the Littlewood–Paley dyadic decomposition is
developed for constructing low-regularity integrators for the one-dimensional cubic …

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 …

We consider various filtered time discretizations of the periodic Korteweg–de Vries equation:
a filtered exponential integrator, a filtered Lie splitting scheme, as well as a filtered …