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
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
The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon Schrodinger equation. The Homotopy analysis solutions of the Klein-Gordon Schrodinger equation contain an auxiliary parame...The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon Schrodinger equation. The Homotopy analysis solutions of the Klein-Gordon Schrodinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution.展开更多
We propose multisymplectic implicit and explicit Fourier pseudospectral methods for the Klein-Gordon-Schrodinger equations.We prove that the implicit method satisfies the charge conservation law exactly.Both methods p...We propose multisymplectic implicit and explicit Fourier pseudospectral methods for the Klein-Gordon-Schrodinger equations.We prove that the implicit method satisfies the charge conservation law exactly.Both methods provide accurate solutions in long-time computations and simulate the soliton collision well.The numerical results show the abilities of the two methods in preserving the charge,energy,and momentum conservation laws.展开更多
This paper concerns the orbital stability for exact solitary waves of the Generalized Klein-Gordon-Schrod-inger equations. Since the abstract results of Grillakis et al[1-2] can not be applied directly, we can extend ...This paper concerns the orbital stability for exact solitary waves of the Generalized Klein-Gordon-Schrod-inger equations. Since the abstract results of Grillakis et al[1-2] can not be applied directly, we can extend the abstract stability theory and use the detailed spectral analysis to obtain the stability of the solitary waves.展开更多
A local energy conservation law is proposed for the Klein--Gordon-Schrrdinger equations, which is held in any local time-space region. The local property is independent of the boundary condition and more essential tha...A local energy conservation law is proposed for the Klein--Gordon-Schrrdinger equations, which is held in any local time-space region. The local property is independent of the boundary condition and more essential than the global energy conservation law. To develop a numerical method preserving the intrinsic properties as much as possible, we propose a local energy-preserving （LEP） scheme for the equations. The merit of the proposed scheme is that the local energy conservation law can hold exactly in any time-space region. With the periodic boundary conditions, the scheme also possesses the discrete change and global energy conservation laws. A nonlinear analysis shows that the LEP scheme converges to the exact solutions with order O（τ2 ＋ h2）. The theoretical properties are verified by numerical experiments.展开更多
K lein-Gordon-Schr d inger(KGS)方程是出现在某些物理问题中一类重要方程,对它的解的理论和有界区域问题的数值解法已有不少研究,但对于无界区域问题的数值方法研究甚少.讨论具弱阻尼的KGS方程的Cauchy问题,采用Chebyshev有理谱方法...K lein-Gordon-Schr d inger(KGS)方程是出现在某些物理问题中一类重要方程,对它的解的理论和有界区域问题的数值解法已有不少研究,但对于无界区域问题的数值方法研究甚少.讨论具弱阻尼的KGS方程的Cauchy问题,采用Chebyshev有理谱方法进行讨论,构造了全离散的Chebyshev有理谱格式,并通过对近似解的一系列先验估计,最后得到了近似解的误差估计.展开更多
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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10735030)National Basic Research Program of China (Grant No. 2007CB814800)+1 种基金Ningbo Natural Science Foundation (Grant No. 2008A610017)K.C. Wong Magna Fund in Ningbo University
文摘The Homotopy analysis method is applied to obtain the approximate solution of the Klein-Gordon Schrodinger equation. The Homotopy analysis solutions of the Klein-Gordon Schrodinger equation contain an auxiliary parameter which provides a convenient way to control the convergence region and rate of the series solutions. Through errors analysis and numerical simulation, we can see the approximate solution is very close to the exact solution.
基金Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11201169)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 10KJB110001)
文摘We propose multisymplectic implicit and explicit Fourier pseudospectral methods for the Klein-Gordon-Schrodinger equations.We prove that the implicit method satisfies the charge conservation law exactly.Both methods provide accurate solutions in long-time computations and simulate the soliton collision well.The numerical results show the abilities of the two methods in preserving the charge,energy,and momentum conservation laws.
文摘This paper concerns the orbital stability for exact solitary waves of the Generalized Klein-Gordon-Schrod-inger equations. Since the abstract results of Grillakis et al[1-2] can not be applied directly, we can extend the abstract stability theory and use the detailed spectral analysis to obtain the stability of the solitary waves.
基金supported by the National Natural Science Foundation of China(Grant Nos.11201169,11271195,and 41231173)the Project of Graduate Education Innovation of Jiangsu Province,China(Grant No.CXLX13 366)
文摘A local energy conservation law is proposed for the Klein--Gordon-Schrrdinger equations, which is held in any local time-space region. The local property is independent of the boundary condition and more essential than the global energy conservation law. To develop a numerical method preserving the intrinsic properties as much as possible, we propose a local energy-preserving （LEP） scheme for the equations. The merit of the proposed scheme is that the local energy conservation law can hold exactly in any time-space region. With the periodic boundary conditions, the scheme also possesses the discrete change and global energy conservation laws. A nonlinear analysis shows that the LEP scheme converges to the exact solutions with order O（τ2 ＋ h2）. The theoretical properties are verified by numerical experiments.
基金This work is supported by National Natural Science Foundation of China under Grant(10771139)Inno-vation Program of Shanghai Municipal Education Commission under Grant(08ZZ70).
文摘K lein-Gordon-Schr d inger(KGS)方程是出现在某些物理问题中一类重要方程,对它的解的理论和有界区域问题的数值解法已有不少研究,但对于无界区域问题的数值方法研究甚少.讨论具弱阻尼的KGS方程的Cauchy问题,采用Chebyshev有理谱方法进行讨论,构造了全离散的Chebyshev有理谱格式,并通过对近似解的一系列先验估计,最后得到了近似解的误差估计.
