We propose an explicit multisymplectic Fourier pseudospectral scheme for the complex modified Korteweg-de Vries equation.Two test problems,the motion of a single solitary wave and interaction of solitary waves,are sim...We propose an explicit multisymplectic Fourier pseudospectral scheme for the complex modified Korteweg-de Vries equation.Two test problems,the motion of a single solitary wave and interaction of solitary waves,are simulated.Numerical experiments show that the present scheme not only provides highly accurate numerical solutions,but also displays good performance in preserving the three integral invariants during long-time computation.Especially,the excellent ability to preserve the higher order invariant indicates that the proposed algorithm is robust and reliable.展开更多
We first note that the improved Boussinesq equation has a multisymplectic structure.Based on it,a multisymplectic scheme is proposed.Dispersion relations analysis and linear stability analysis show that the proposed s...We first note that the improved Boussinesq equation has a multisymplectic structure.Based on it,a multisymplectic scheme is proposed.Dispersion relations analysis and linear stability analysis show that the proposed scheme has excellent properties.Numerical results confirm the excellent long-term behavior of the proposed scheme.展开更多
Applying the Fourier pseudospectral method to space derivatives and the symplectic Euler rule to time derivatives in the multisymplectic form of the Klein–Gordon–Zakharov equations,we derive an explicit multisymplec...Applying the Fourier pseudospectral method to space derivatives and the symplectic Euler rule to time derivatives in the multisymplectic form of the Klein–Gordon–Zakharov equations,we derive an explicit multisymplectic scheme.The semi-discrete energy and momentum conservation laws are given.Some numerical experiments are carried out to show the accuracy of the numerical solutions.The performance of the scheme in preserving the global energy and momentum conservation laws are also checked.展开更多
基金Supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No 10KJB110001the Program for Excellent Talents in Huaiyin Normal University(No 11HSQNZ01)。
文摘We propose an explicit multisymplectic Fourier pseudospectral scheme for the complex modified Korteweg-de Vries equation.Two test problems,the motion of a single solitary wave and interaction of solitary waves,are simulated.Numerical experiments show that the present scheme not only provides highly accurate numerical solutions,but also displays good performance in preserving the three integral invariants during long-time computation.Especially,the excellent ability to preserve the higher order invariant indicates that the proposed algorithm is robust and reliable.
基金Supported by the National Natural Science Foundation of China under Grant No 11201169the Project of Graduate Education Innovation of Jiangsu Provience under Grant No CXLX13_366+1 种基金the Natural Science Foundation of Jiangsu Education Institution under Grant No 12KJB110002the Qing Lan Project of Jiangsu Province.
文摘We first note that the improved Boussinesq equation has a multisymplectic structure.Based on it,a multisymplectic scheme is proposed.Dispersion relations analysis and linear stability analysis show that the proposed scheme has excellent properties.Numerical results confirm the excellent long-term behavior of the proposed scheme.
基金Supported by the Natural Science Foundation of Jiangsu Higher Education Institutions of China under Grant No 10KJB110001the Program for Excellent Talents in Huaiyin Normal University(No 11HSQNZ01).
文摘Applying the Fourier pseudospectral method to space derivatives and the symplectic Euler rule to time derivatives in the multisymplectic form of the Klein–Gordon–Zakharov equations,we derive an explicit multisymplectic scheme.The semi-discrete energy and momentum conservation laws are given.Some numerical experiments are carried out to show the accuracy of the numerical solutions.The performance of the scheme in preserving the global energy and momentum conservation laws are also checked.
