A Conservative Local Discontinuous Galerkin Method for the Schrödinger-KdV System (Communications in Computational Physics, 2020)
In this paper we develop a conservative local discontinuous Galerkin (LDG)method for the Schrödinger-Korteweg-de Vries (Sch-KdV) system, which arises in variousphysical contexts as a model for the interaction of long and short nonlinear waves.Conservative quantities in the discrete version of the number of plasmons, energy ofthe oscillations and the number of particles are proved for the LDG scheme of theSch-KdV system. Semi-implicit time discretization is adopted to relax the time stepconstraint from the high order spatial derivatives. Numerical results for accuracy testsof stationary traveling soliton, and the collision of solitons are shown. Numerical experimentsillustrate the accuracy and capability of the method.