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

Published online by Cambridge University Press:  03 June 2015

Yinhua Xia  and
Yan Xu
Yinhua Xia*
Affiliation:
School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China
Yan Xu*
Affiliation:
School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China
*
Corresponding author.Email:yhxia@ustc.edu.cn
Email:yxu@ustc.edu.cn
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Abstract

In this paper we develop a conservative local discontinuous Galerkin (LDG) method for the Schrödinger-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.

Keywords

65M6035Q5335Q55Schrödinger-KdV systemthe conservative local discontinuous Galerkin methodsemi-implicit time discretizationconservative quantities
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 4 , April 2014 , pp. 1091 - 1107
Copyright
Copyright © Global Science Press Limited 2014

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