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 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 Hʳ(T) for the initial data in Hʳ⁺⁴(T) with $r>1/2$. Furthermore, the third-order convergence in L²(T) is established for the initial data in H⁴(T). Numerical experiments are presented to confirm the theoretical convergence results.