Local structure-preserving algorithms for the nonlinear Schrödinger equation with power law nonlinearity

This paper introduces three local structure-preserving algorithms for the one-dimensional nonlinear Schrödinger equation with power law nonlinearity, comprising two local energy-conserving algorithms and one local momentum-conserving algorithm. Additionally, we extend these local conservation algorithms to achieve global conservation under periodic boundary conditions. Theoretical analyses confirm the conservation properties of these algorithms. In numerical experiments, we validate the advantages of these algorithms in maintaining long-term energy or momentum conservation by comparing them with a multi-symplectic Preissman algorithm.