分裂高精度法求解非线性薛定谔方程
发布时间：2018-09-04 16:48
【摘要】：针对描述玻色爱因斯坦凝聚体(Bose-Einstein condensates,BEC)动力学行为的二维非线性薛定谔方程(nonlinear Schr銉dinger equations,NLSE)的求解,首先基于算符分裂思想将方程分裂为2个子齐次方程,然后基于分步有限差分法提出一种在空间上具有四阶精度的分裂高精度方法,最后利用存在精确解析解的二维NLSE分析该方法的精度和收敛性,同时对不存在精确解析解的二维BEC系统进行数值模拟.结果表明,在一类特殊的初始条件下,随着时间的延长,涡旋晶格自由扩散,涡旋结构则对称扩散.
[Abstract]:In order to solve the two-dimensional nonlinear Schrodinger equation (nonlinear Schr dinger equations,NLSE, which describes the dynamical behavior of the Bose-Einstein condensate (Bose-Einstein condensates,BEC), the equation is first split into two sub-homogeneous equations based on the idea of operator splitting. Then, based on the step finite difference method, a split high precision method with fourth order accuracy in space is proposed. Finally, the accuracy and convergence of the method are analyzed by using two-dimensional NLSE with exact analytical solutions. At the same time, the numerical simulation of two-dimensional BEC system without exact analytical solution is carried out. The results show that the vortex lattice diffuses freely and the vortex structure propagates symmetrically with the prolongation of time under a special initial condition.
【作者单位】： 扬州大学数学科学学院;
【基金】：国家自然科学基金资助项目(11501495) 江苏省自然科学基金资助项目(BK20150436) 江苏省高校面上基金资助项目(15KJB110025) 江苏省大学生科技创新项目(201611117016Z) 扬州大学创新创业教育改革项目(yzucx2016-2C)
【分类号】：O175.29
本文编号：2222767
[Abstract]:In order to solve the two-dimensional nonlinear Schrodinger equation (nonlinear Schr dinger equations,NLSE, which describes the dynamical behavior of the Bose-Einstein condensate (Bose-Einstein condensates,BEC), the equation is first split into two sub-homogeneous equations based on the idea of operator splitting. Then, based on the step finite difference method, a split high precision method with fourth order accuracy in space is proposed. Finally, the accuracy and convergence of the method are analyzed by using two-dimensional NLSE with exact analytical solutions. At the same time, the numerical simulation of two-dimensional BEC system without exact analytical solution is carried out. The results show that the vortex lattice diffuses freely and the vortex structure propagates symmetrically with the prolongation of time under a special initial condition.
【作者单位】： 扬州大学数学科学学院;
【基金】：国家自然科学基金资助项目(11501495) 江苏省自然科学基金资助项目(BK20150436) 江苏省高校面上基金资助项目(15KJB110025) 江苏省大学生科技创新项目(201611117016Z) 扬州大学创新创业教育改革项目(yzucx2016-2C)
【分类号】：O175.29
【相似文献】
相关期刊论文 前4条
1 张睿;王军帽;韩家骅;;一类非线性薛定谔方程的精确解析解[J];安徽大学学报(自然科学版);2009年03期
2 许晓革;Caudrey-Dodd-Gibbon-Sawada-Kotera方程的一类精确解析解[J];北京机械工业学院学报;2005年02期
3 黄炎;;矩形薄板弹性弯曲的精确解析解法[J];工程力学;1986年02期
4 尚亚东,高帆;非线性耦合标量场方程的精确解析解[J];西安石油学院学报(自然科学版);2002年04期
，本文编号：2222767
本文链接：https://www.wllwen.com/kejilunwen/yysx/2222767.html
