Novel high-order explicit energy-preserving schemes for NLS-type equations based on the Lie-group method

In this paper, by taking the NLS-type equations as examples, we propose a novel high -order explicit energy -preserving Lie -group method for Hamiltonian PDEs. The main idea is to combine recently developed generalized SAV (G-SAV) approach (Cheng et al., 2021) and explicit Lie group method, in which the fourth -order or higher -order Lie group method only composes two exponentials in each stage, and this is the key point that the proposed methods can preserve energy of Hamiltonian PDEs. This is our first attempt to construct high -order explicit energypreserving methods without using projection technique (Hairer et al., 2006 [14]), and some stability conclusions of our proposed methods for the NLS-type equations are also presented. Finally, we present 2D and 3D numerical simulations to demonstrate the stability and accuracy.