Meshless symplectic and multi-symplectic scheme for the coupled nonlinear Schrödinger system based on local RBF approximation. (15th March 2023) - Zhang, Shengliang
Abstract: In this paper, a new meshless symplectic and multi-symplectic scheme is developed for solving the coupled nonlinear Schrödinger system. The key feature of the method is the utilization of local radial basis function (RBF) approximation (LRBFA) method in spatial discretization. The LRBFA only requires solving a small linear system, thus it can circumvent the ill-conditioned problem and shape-parameter-sensitivity of global RBF method. The proposed method offers a high order of convergence and conserves the invariants well. Various numerical examples are presented to verify that the proposed method is valid for both uniform knots and random knots.