An explicit third-order low-regularity integrator for the cubic nonlinear Schrödinger equation

In this paper, we propose an explicit third-order low-regularity integrator for the cubic nonlinear Schrödinger equation on the one-dimensional torus $\mathbb{T}$. By carefully designing numerical approximations for the integrals in Fourier space, we construct a third-order scheme and provide a rigorous global error analysis. More precisely, we prove that the scheme achieves third-order convergence in $H^{r}(\mathbb{T})$ for the initial data in $H^{r+4}(\mathbb{T})$ with $r>1/2$. Furthermore, the third-order convergence in $L^{2}(\mathbb{T})$ is established for the initial data in $H^{4}(\mathbb{T})$. Numerical experiments are presented to confirm the theoretical convergence results.