TY - JOUR T1 - Fourth Order Exponential Time Differencing Method with Local Discontinuous Galerkin Approximation for Coupled Nonlinear Schrödinger Equations JO - Communications in Computational Physics VL - 2 SP - 510 EP - 541 PY - 2018 DA - 2018/04 SN - 17 DO - http://doi.org/10.4208/cicp.060414.190914a UR - https://global-sci.org/intro/article_detail/cicp/10967.html KW - AB -

This paper studies a local discontinuous Galerkin method combined with fourth order exponential time differencing Runge-Kutta time discretization and a fourth order conservative method for solving the nonlinear Schrödinger equations. Based on different choices of numerical fluxes, we propose both energy-conserving and energy-dissipative local discontinuous Galerkin methods, and have proven the error estimates for the semi-discrete methods applied to linear Schrödinger equation. The numerical methods are proven to be highly efficient and stable for long-range soliton computations. Extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.