In this paper, a novel multisymplectic scheme is proposed for the coupled nonlinear Schrodinger-KdV （CNLS-KdV） equations. The CNLS-KdV equations are rewritten into the multisymplectic Hamiltonian form by introducing...In this paper, a novel multisymplectic scheme is proposed for the coupled nonlinear Schrodinger-KdV （CNLS-KdV） equations. The CNLS-KdV equations are rewritten into the multisymplectic Hamiltonian form by introducing some canonical momenta. To simulate the problem efficiently, the CNLS-KdV equations are approximated by a high order compact method in space which preserves N semi-discrete multisymplectic conservation laws. We then discretize the semi-discrete system by using a symplectic midpoint scheme in time. Thus, a full-discrete multisymplectic scheme is obtained for the CNLS-KdV equations. The conservation laws of the full-discrete scheme are analyzed. Some numerical experiments are presented to further verify the convergence and conservation laws of the new scheme.展开更多
We study the Schrodinger-KdV system{-△u+λ1(x)u=u^3+βuv,u∈H^1(R^N),-△v+λ2(x)v=1/2v^2+β/2u^2,v∈H^1(R^N),where N=1,2,3,λi(x)∈C(R^N,R),lim|x|→∞λi(x)=λi(∞),and λi(x)≤λi(∞),i=1,2,a.e.x∈R^N.We obtain the ...We study the Schrodinger-KdV system{-△u+λ1(x)u=u^3+βuv,u∈H^1(R^N),-△v+λ2(x)v=1/2v^2+β/2u^2,v∈H^1(R^N),where N=1,2,3,λi(x)∈C(R^N,R),lim|x|→∞λi(x)=λi(∞),and λi(x)≤λi(∞),i=1,2,a.e.x∈R^N.We obtain the existence of nontrivial ground state solutions for the above system by variational methods and the Nehari manifold.展开更多
This paper is devoted to the study of the Cauchy problem for the coupled system of the Schrodinger-KdV equations which describes the nonlinear dynamics of the one-dimensional Langmuir and ion-acoustic waves. Global we...This paper is devoted to the study of the Cauchy problem for the coupled system of the Schrodinger-KdV equations which describes the nonlinear dynamics of the one-dimensional Langmuir and ion-acoustic waves. Global well-posedness of the problem is established in the space H^k×H^k (k∈ Z^+), the first and second components of which correspond to the electric field of the Langmuir oscillations and the low-frequency density perturbation respectively.展开更多
The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction di...The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.展开更多
基金This work is supported by the NNSFC （Nos. 11771213, 41504078, 11301234, 11271171）, the National Key Research and Development Project of China （No. 2016YFC0600310）, the Major Projects of Natural Sciences of University in Jiangsu Province of China （No. 15KJA110002） and the Priority Academic Program Development of Jiangsu Higher Education Institutions, the Provincial Natural Science Foundation of Jiangxi （Nos. 20161ACB20006, 20142BCB23009, 20151BAB 201012）.
文摘In this paper, a novel multisymplectic scheme is proposed for the coupled nonlinear Schrodinger-KdV （CNLS-KdV） equations. The CNLS-KdV equations are rewritten into the multisymplectic Hamiltonian form by introducing some canonical momenta. To simulate the problem efficiently, the CNLS-KdV equations are approximated by a high order compact method in space which preserves N semi-discrete multisymplectic conservation laws. We then discretize the semi-discrete system by using a symplectic midpoint scheme in time. Thus, a full-discrete multisymplectic scheme is obtained for the CNLS-KdV equations. The conservation laws of the full-discrete scheme are analyzed. Some numerical experiments are presented to further verify the convergence and conservation laws of the new scheme.
基金supportedby the National Natural Science Foundation of China(Grant No.11971393).
文摘We study the Schrodinger-KdV system{-△u+λ1(x)u=u^3+βuv,u∈H^1(R^N),-△v+λ2(x)v=1/2v^2+β/2u^2,v∈H^1(R^N),where N=1,2,3,λi(x)∈C(R^N,R),lim|x|→∞λi(x)=λi(∞),and λi(x)≤λi(∞),i=1,2,a.e.x∈R^N.We obtain the existence of nontrivial ground state solutions for the above system by variational methods and the Nehari manifold.
基金Supported by the National Natural Science Foundation of Chinathe NSF of China Academy of Engineering Physics
文摘This paper is devoted to the study of the Cauchy problem for the coupled system of the Schrodinger-KdV equations which describes the nonlinear dynamics of the one-dimensional Langmuir and ion-acoustic waves. Global well-posedness of the problem is established in the space H^k×H^k (k∈ Z^+), the first and second components of which correspond to the electric field of the Langmuir oscillations and the low-frequency density perturbation respectively.
基金Supported by the NNSFC(11301234,11271171,11101399)the Provincial Natural Science Foundation of Jiangxi(20142BCB23009,20151BAB201012)State Key Laboratory of Scientific and Engineering Computing,CAS,and Jiangsu Key Lab for NSLSCS(201302)
基金supported by the National Natural Science Foundation of China(Grant No.91130013)the Open Foundation of State Key Laboratory of HighPerformance Computing of China
文摘The energy preserving average vector field （AVF） method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.
基金Supported by the Chinese National Science Foundation for Distinguished Young Scholars(No. 10671153)Research Foundation of Northwest University,China(No.09NW023) respectively
