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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 Schrdinger 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.  相似文献   
2.
The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear Schrödinger 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.  相似文献   
3.
采用双曲函数展开法得到Modified Benjamin-Bona-Mahony(mBBM)方程的一类扭结-反扭结状的双扭结孤立波解,在不同的极限情况下,此孤立波分别退化为mBBM方程的扭结状和钟状孤立波解.对双扭结型单孤子的结构特征进行分析,构造有限差分格式对其动力学稳定性进行数值研究.有限差分格式为两层隐式格式,在线性化意义下无条件稳定.数值结果表明mBBM方程的双扭结型单孤子在不同类型的扰动下均具有很强的稳定性.对双孤立波的碰撞进行数值模拟,发现既存在弹性碰撞也存在非弹性碰撞.  相似文献   
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