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Volume 15, Issue 4
A Conservative Local Discontinuous Galerkin Method for the Schrödinger-KdV System

Yinhua Xia & Yan Xu

DOI: 10.4208/cicp.140313.160813s

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

Published online: 2014-04

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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.

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@Article{CiCP-15-1091, author = {Yinhua Xia and Yan Xu}, title = {A Conservative Local Discontinuous Galerkin Method for the Schrödinger-KdV System}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {4}, pages = {1091--1107}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.140313.160813s}, url = {http://global-sci.org/intro/article_detail/cicp/7129.html} }
TY - JOUR T1 - A Conservative Local Discontinuous Galerkin Method for the Schrödinger-KdV System AU - Yinhua Xia & Yan Xu JO - Communications in Computational Physics VL - 4 SP - 1091 EP - 1107 PY - 2014 DA - 2014/04 SN - 15 DO - http://doi.org/10.4208/cicp.140313.160813s UR - https://global-sci.org/intro/article_detail/cicp/7129.html KW - AB -

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.

Yinhua Xia and Yan Xu. (2014). A Conservative Local Discontinuous Galerkin Method for the Schrödinger-KdV System. Communications in Computational Physics. 15 (4). 1091-1107. doi:10.4208/cicp.140313.160813s
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