Time-relaxation structure-preserving explicit low-regularity integrators for the nonlinear Schr\"odinger equation

Abstract

We propose and rigorously analyze a novel family of explicit low-regularity exponential integrators for the nonlinear Schr\"odinger (NLS) equation, based on a time-relaxation framework. The methods combine a resonance-based scheme for the twisted variable with a dynamically adjusted relaxation parameter that guarantees exact mass conservation. Unlike existing symmetric or structure-preserving low-regularity integrators, which are typically implicit and computationally expensive, the proposed methods are fully explicit, mass-conserving, and well-suited for solutions with low regularity. Furthermore, the schemes can be naturally extended to a broad class of evolution equations exhibiting the structure of strongly continuous contraction semigroups. Numerical results demonstrate the accuracy, robustness, and excellent long-time behavior of the methods under low-regularity conditions.