讨论了 Klein- Gordon方程组utt-Δu +α2 u +a2 uv2 =f (x,t) ,vtt-Δ v +β2 v +b2 u2 v =g(x,t)初边值问题的经典解 ,这里 f (x,t) ,g(x,t)为实值函数 ,α,β,a,b都为常数 .应用 Galerkin方法得到了上述耦合方程组在 Rn(1≤ n≤ 3)
The final value problem for the classical coupled Klein-Gordon-Schrodinger equations is studied in . This leads to the construction of the modified wave operator Ω, for certain scattered data. When initial functions ...The final value problem for the classical coupled Klein-Gordon-Schrodinger equations is studied in . This leads to the construction of the modified wave operator Ω, for certain scattered data. When initial functions belong to (Ω) which denotes the range domain of Ω, the global existence and asymptotic behavior of solutions of Cauchy problem tor the coupled Klein-Gordon-Schrodinger equations are proved.展开更多
A multisymplectic Fourier pseudo-spectral scheme, which exactly preserves the discrete multisym- plectic conservation law, is presented to solve the Klein-Gordon-SchrSdinger equations. The scheme is of spectral accura...A multisymplectic Fourier pseudo-spectral scheme, which exactly preserves the discrete multisym- plectic conservation law, is presented to solve the Klein-Gordon-SchrSdinger equations. The scheme is of spectral accuracy in space and of second order in time. The scheme preserves the discrete multisymplectic conservation law and the charge conservation law. Moreover, the residuals of some other conservation laws are derived for the geometric numerical integrator. Extensive numerical simulations illustrate the numerical behavior of the multisymplectic scheme, and demonstrate the correctness of the theoretical analysis.展开更多
In this paper,we consider the energy conserving numerical scheme for coupled nonlinear Klein-Gordon equations.We propose energy conserving finite element method and get the unconditional superconvergence resultO(h^(2)...In this paper,we consider the energy conserving numerical scheme for coupled nonlinear Klein-Gordon equations.We propose energy conserving finite element method and get the unconditional superconvergence resultO(h^(2)+Dt^(2))by using the error splitting technique and postprocessing interpolation.Numerical experiments are carried out to support our theoretical results.展开更多
In this article,we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the...In this article,we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the modified simple equation method.The proposed method is so powerful and effective to solve nonlinear space-time fractional differential equations by with modified Riemann–Liouville derivative.展开更多
We present an extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics. By using extended F-expansion method, many periodic wave solutions expressed by v...We present an extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics. By using extended F-expansion method, many periodic wave solutions expressed by various Jacobi elliptic functions for the Klein-Gordon-Schrodinger equations are obtained. In the limit cases, the solitary wave solutions and trigonometric function solutions for the equations are also obtained.展开更多
文摘讨论了 Klein- Gordon方程组utt-Δu +α2 u +a2 uv2 =f (x,t) ,vtt-Δ v +β2 v +b2 u2 v =g(x,t)初边值问题的经典解 ,这里 f (x,t) ,g(x,t)为实值函数 ,α,β,a,b都为常数 .应用 Galerkin方法得到了上述耦合方程组在 Rn(1≤ n≤ 3)
基金the National Natural Science Foundation of China
文摘The final value problem for the classical coupled Klein-Gordon-Schrodinger equations is studied in . This leads to the construction of the modified wave operator Ω, for certain scattered data. When initial functions belong to (Ω) which denotes the range domain of Ω, the global existence and asymptotic behavior of solutions of Cauchy problem tor the coupled Klein-Gordon-Schrodinger equations are proved.
基金supported by National Natural Science Foundation of China(Grant Nos.10901074,11271171,91130003,11001009 and 11101399)the Province Natural Science Foundation of Jiangxi(Grant No. 20114BAB201011)+2 种基金the Foundation of Department of Education of Jiangxi Province(Grant No.GJJ12174)the State Key Laboratory of Scientific and Engineering Computing,CASsupported by the Youth Growing Foundation of Jiangxi Normal University in 2010
文摘A multisymplectic Fourier pseudo-spectral scheme, which exactly preserves the discrete multisym- plectic conservation law, is presented to solve the Klein-Gordon-SchrSdinger equations. The scheme is of spectral accuracy in space and of second order in time. The scheme preserves the discrete multisymplectic conservation law and the charge conservation law. Moreover, the residuals of some other conservation laws are derived for the geometric numerical integrator. Extensive numerical simulations illustrate the numerical behavior of the multisymplectic scheme, and demonstrate the correctness of the theoretical analysis.
基金The work is supported by the National Natural Science Foundation of China(No.11871441)Beijing Natural Science Foundation(No.1192003).
文摘In this paper,we consider the energy conserving numerical scheme for coupled nonlinear Klein-Gordon equations.We propose energy conserving finite element method and get the unconditional superconvergence resultO(h^(2)+Dt^(2))by using the error splitting technique and postprocessing interpolation.Numerical experiments are carried out to support our theoretical results.
文摘In this article,we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the modified simple equation method.The proposed method is so powerful and effective to solve nonlinear space-time fractional differential equations by with modified Riemann–Liouville derivative.
基金The project supported by the Natural Science Foundation of Eduction Committce of Henan Province of China under Grant No. 2003110003, and the Science Foundation of Henan University of Science and Technology under Grant Nos. 2004ZD002 and 2004ZY040
文摘We present an extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics. By using extended F-expansion method, many periodic wave solutions expressed by various Jacobi elliptic functions for the Klein-Gordon-Schrodinger equations are obtained. In the limit cases, the solitary wave solutions and trigonometric function solutions for the equations are also obtained.