A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrödinger Equations with Multiply Components

Abstract

Considering the coupled nonlinear Schrödinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations. Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.

Novel High-Order Mass- and Energy-Conservative Runge-Kutta Integrators for the Regularized Logarithmic Schrödinger Equation

“…There have been many theoretical and numerical studies of structure-preserving discretizations for the NLSE with power-like nonlinearity, including symplectic and multi-symplectic methods [15,39,51], conservative Crank-Nicolson methods [23,31], and splitting methods [29,41]. The increased interest in this subject can mainly be attributed to the superior qualitative behavior over long time integration of such methods.…”