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 lon...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.展开更多
基金supported by the NSFC projects No.11101400Doctoral Fund of Ministry of Education of China No.20113402120015+1 种基金SRF for ROCS SEM.Research of Y.Xu is supported by NSFC grant No.10971211,No.11031007,FANEDD No.200916,NCET No.09-0922Fok Ying Tung Education Foundation No.131003.
文摘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.
