Novel Conformal Structure-Preserving Algorithms for Coupled Damped Nonlinear Schrödinger System (Advances in Applied Mathematics and Mechanics, 2021)
This paper introduces two novel conformal structure-preserving algorithmsfor solving the coupled damped nonlinear Schrödinger (CDNLS) system, which arebased on the conformal multi-symplectic Hamiltonian formulation and its conformalconservation laws. The proposed algorithms can preserve corresponding conformalmulti-symplectic conservation law and conformal momentum conservation law in anylocal time-space region, respectively. Moreover, it is further shown that the algorithmsadmit the conformal charge conservation law, and exactly preserve the dissipationrate of charge under appropriate boundary conditions. Numerical experiments are presentedto demonstrate the conformal properties and effectiveness of the proposedalgorithms during long-time numerical simulations and validate the analysis.