A Conservative Local Discontinuous Galerkin Method for the Schro ̈ dinger-KdV System

Yinhua Xia University of Science and Technology of China Yan Xu University of Science and Technology of China

Numerical Analysis and Scientific Computing mathscidoc:1612.25009

Communication in Computational Physic, 15, (4), 1091-1107, 2014.4
InthispaperwedevelopaconservativelocaldiscontinuousGalerkin(LDG) method for the Schro ̈ dinger-Korteweg-de Vries (Sch-KdV) system, which arises in var- ious 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 ex- periments illustrate the accuracy and capability of the method.
Schro ̈dinger-KdV system, the conservative local discontinuous Galerkin method, semi-implicit time discretization, conservative quantities.
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@inproceedings{yinhua2014a,
  title={A Conservative Local Discontinuous Galerkin Method for the Schro ̈ dinger-KdV System},
  author={Yinhua Xia, and Yan Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161231220709885587705},
  booktitle={Communication in Computational Physic},
  volume={15},
  number={4},
  pages={1091-1107},
  year={2014},
}
Yinhua Xia, and Yan Xu. A Conservative Local Discontinuous Galerkin Method for the Schro ̈ dinger-KdV System. 2014. Vol. 15. In Communication in Computational Physic. pp.1091-1107. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161231220709885587705.
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