we theoretically investigated the transverse instability of three-dimensional（3D）dust-acoustic solitary waves in a magnetized dusty plasma.First,a 3D nonlinear ZakharovKuznetsov（ZK）equation,which can be used to de...we theoretically investigated the transverse instability of three-dimensional（3D）dust-acoustic solitary waves in a magnetized dusty plasma.First,a 3D nonlinear ZakharovKuznetsov（ZK）equation,which can be used to describe the time-evolution of dust-acoustic solitary waves in magnetized dusty plasmas,is derived by using the reductive perturbation method.Second,we established a numerical scheme to study the transverse instability of the solitary waves described by the ZK equation.It was found that both stable and unstable solitary waves exist.展开更多
The Homotopy analysis method （HAM） is adopted to find the approximate analytical solutions of the Gross- Pitaevskii equation, a nonlinear Schrodinger equation is used in simulation of Bose-Einstein condensates trapp...The Homotopy analysis method （HAM） is adopted to find the approximate analytical solutions of the Gross- Pitaevskii equation, a nonlinear Schrodinger equation is used in simulation of Bose-Einstein condensates trapped in a harmonic potential. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they fit very well with each other when the atomic interaction is weak.展开更多
We try to find the analytical solutions to the time-independent Gross-Pitaevskii equation,a nonlinear Schrodinger equation used in the simulation of Bose–Einstein condensates trapped in a harmonic potential.Both the ...We try to find the analytical solutions to the time-independent Gross-Pitaevskii equation,a nonlinear Schrodinger equation used in the simulation of Bose–Einstein condensates trapped in a harmonic potential.Both the homotopy analysis method and the Galerkin spectral method are applied.We investigate the one-dimensional case and obtain the approximate analytical solutions successfully.Comparison between the analytical solutions and the numerical solutions has been made.The results indicate that they agree very well with each other when the atomic interaction is not too strong.展开更多
Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation,a nonlinear Schrdinger equation used ...Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation,a nonlinear Schrdinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential.The approximate analytical solutions are obtained successfully.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.展开更多
The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear SchrSdinger equation used in simulation of spin-1 Bose-Eins...The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear SchrSdinger equation used in simulation of spin-1 Bose-Einstein condensates trapped in a harmonic potential. We investigate the one-dimensional case and get the approximate analytical solutions successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are in agreement well with each other when the atomic interaction is weakly. We also find a class of exact solutions for the stationary states of the spin-1 system with harmonic potential for a special case.展开更多
基金supported by National Natural Science Foundation of China(No.11047010)
文摘we theoretically investigated the transverse instability of three-dimensional（3D）dust-acoustic solitary waves in a magnetized dusty plasma.First,a 3D nonlinear ZakharovKuznetsov（ZK）equation,which can be used to describe the time-evolution of dust-acoustic solitary waves in magnetized dusty plasmas,is derived by using the reductive perturbation method.Second,we established a numerical scheme to study the transverse instability of the solitary waves described by the ZK equation.It was found that both stable and unstable solitary waves exist.
基金Project supported by the National Natural Science Foundation of China(Grant No.11047010)the Key Project Foundation of the Education Ministry of China(Grant No.209128)
文摘The Homotopy analysis method （HAM） is adopted to find the approximate analytical solutions of the Gross- Pitaevskii equation, a nonlinear Schrodinger equation is used in simulation of Bose-Einstein condensates trapped in a harmonic potential. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they fit very well with each other when the atomic interaction is weak.
基金Supported by the National Natural Science Foundation under Grant No 11047010the Key Project Foundation of the Education Ministry of China under Grant No 209128。
文摘We try to find the analytical solutions to the time-independent Gross-Pitaevskii equation,a nonlinear Schrodinger equation used in the simulation of Bose–Einstein condensates trapped in a harmonic potential.Both the homotopy analysis method and the Galerkin spectral method are applied.We investigate the one-dimensional case and obtain the approximate analytical solutions successfully.Comparison between the analytical solutions and the numerical solutions has been made.The results indicate that they agree very well with each other when the atomic interaction is not too strong.
基金Supported by the National Natural Science Foundation under Grant No. 11047010
文摘Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation,a nonlinear Schrdinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential.The approximate analytical solutions are obtained successfully.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China under Grant No. 11047010.
文摘The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear SchrSdinger equation used in simulation of spin-1 Bose-Einstein condensates trapped in a harmonic potential. We investigate the one-dimensional case and get the approximate analytical solutions successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are in agreement well with each other when the atomic interaction is weakly. We also find a class of exact solutions for the stationary states of the spin-1 system with harmonic potential for a special case.
