Commun. Comput. Phys., 15 (2014), pp. 1091-1107.


A Conservative Local Discontinuous Galerkin Method for the Schrodinger-KdV System

Yinhua Xia 1*, Yan Xu 1

1 School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China.

Received 14 March 2013; Accepted (in revised version) 16 August 2013
Available online 21 January 2014
doi:10.4208/cicp.140313.160813s

Abstract

In this paper we develop a conservative local discontinuous Galerkin (LDG) method for the Schrodinger-Korteweg-de Vries (Sch-KdV) system, which arises in various physical 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 of the oscillations and the number of particles are proved for the LDG scheme of the Sch-KdV system. Semi-implicit time discretization is adopted to relax the time step constraint from the high order spatial derivatives. Numerical results for accuracy tests of stationary traveling soliton, and the collision of solitons are shown. Numerical experiments illustrate the accuracy and capability of the method.

AMS subject classifications: 65M60, 35Q53, 35Q55

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Key words: Schrodinger-KdV system, the conservative local discontinuous Galerkin method, semi-implicit time discretization, conservative quantities.

*Corresponding author.
Email: yhxia@ustc.edu.cn (Y. Xia), yxu@ustc.edu.cn (Y. Xu)
 

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