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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   
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组合KdV方程的显式精确解   总被引:41,自引:0,他引:41       下载免费PDF全文
借助计算机代数系统Mathematica,利用双曲函数法找到了组合KdV方程(Combined KdV Equation)的精确孤立波解,包括钟型孤立波解和扭结型孤立波解.在此基础上又对双曲函数法的思想进行了推广,从而获得了其更多的显式精确解,包括间断型激波解和指数函数型解.这种方法也适用于求解其他非线性发展方程(组). 关键词: 组合KdV方程 双曲函数法 孤立波解 精确解  相似文献   
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利用同伦分析法求解了Burgers方程,得到了其扭结形孤立波的近似解析解,该解非常接近于相应的精确解.结果表明,同伦分析法可用来求解非线性演化方程的孤立波解.同时,也对所用方法进行了一定扩展,得到了Kadomtsev-Petviashvili(KP)方程的钟形孤立子解.经过扩展后的方法能够更方便地用于求解更多非线性演化方程的高精度近似解析解. 关键词: Burgers方程 同伦分析法 KP方程 孤立波解  相似文献   
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A target in layered medium can be located by the ridge-like distribution time reversal and reverse time migration(TR-RTM) mixed method. However, this method cannot distinguish between acoustic field distributions of the interface and target for the wider acoustic pulse signals, which may result in inaccurate location of the target. A snapshot TR-RTM mixed method is proposed to solve this problem. The principle of snapshot TR-RTM mixed method is first given. Experiments are then carried out, and a mountain-like acoustic field distribution is obtained by processing experimental data. The results show that the location of the peak is that of the target, and the ratio of the scattered signal and interface reflection signal(signal-to-interference ratio) is improved by about four times after processing. Furthermore, this method can effectively suppress the interface reflection signal and enhance the target scattering signal. Therefore, it can achieve effective detection and location of a target in a layered medium.  相似文献   
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对有空气阻尼的非弹性蹦球的动力学行为进行了数值模拟,通过改变控制参数V0,蹦球的运动表现出倍周期分岔、混沌等非线性现象,采用0-1检测法和最大Lyapunov指数证实了这种现象.  相似文献   
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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   
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利用同伦分析法求解了KdV-Burgers方程,得到了它的解析近似解,该解与精确解符合得非常好.结果表明同伦分析法在求解某些耗散系统时,仍然是一种行之有效的方法.  相似文献   
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感应电流方向的正确判定杨红娟(云南省建筑材料工业学校昆明650102)楞次定律和右手定则是确定感应电流方向的两种基本方法,下面就如何正确应用这两种方法作一讨论.1正确应用楞次定律判定感应电流的方向1.1应用楞次定律的步骤1.1.1确定穿过线圈原来磁通...  相似文献   
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快照的时间反转和逆时偏移方法已实现了液-液分层介质中目标的超声检测和定位,现进一步推广到含有固体分层介质情形。由于在含有固体分层介质中,都存在多种的反射波和散射波,因此提出一种筛选方法,首先从中筛选出散射波以及所属波型,再利用快照的时间反转和逆时偏移方法进行处理。实验分别研究了固-液、液-固和固-固分层介质3种情况。利用快照的时间反转和逆时偏移法进行处理,在空间就形成了一个峰状的分布,其峰顶的位置与实际目标的位置比较吻合,误差在一个波长左右。因而,实现了含有固体分层介质中目标的超声检测和定位。   相似文献   
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