| 具阻尼的Gross-Pitaevskii(GP)方程在二维空间中的稳定性 |
| |
| 引用本文： | 舒级,张健.具阻尼的Gross-Pitaevskii(GP)方程在二维空间中的稳定性[J].数学进展,2007,36(4):453-458. |
| |
| 作者姓名： | 舒级 张健 |
| |
| 作者单位： | 1. 四川师范大学计算机软件实验室,成都,四川,610066;四川师范大学数学与软件科学学院,成都,四川,610066;四川大学数学学院,成都,四川,610064
2. 四川师范大学数学与软件科学学院,成都,四川,610066 |
| |
| 摘 要： | 本文讨论出现在吸引玻色-爱因斯坦凝聚中的一类带调和势的阻尼非线性Schr dinger方程.对照玻色-爱因斯坦凝聚的物理性质,证明了阻尼参数存在一个门槛值,即当阻尼参数大于该门槛值时,初值问题的解整体存在;当阻尼参数小于该门槛值时,其初值问题的解将在有限时间内坍塌.
|
| 关 键 词： | 玻色-爱因斯坦凝聚 Schr(o)dinger方程 调和势 阻尼 Gross-Pitaevskii(GP)方程 |
| 文章编号： | 1000-0917（2007）04-0453-06 |
| 修稿时间： | 2004-12-13 |
Stability of Damped Gross-Pitaevskii(GP) Equation in Two-dimensional Spaces |
| |
| SHU Ji,ZHANG Jian.Stability of Damped Gross-Pitaevskii(GP) Equation in Two-dimensional Spaces[J].Advances in Mathematics,2007,36(4):453-458. |
| |
| Authors: | SHU Ji ZHANG Jian |
| |
| Institution: | 1. Sichuan Provincial Key Laboratory of Computer Software, Sichuan Normal University, Chengdu, Sichuan, 610066, P. R. China; 2. College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan, 610066, P. R. China; 3. College of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, P. R. China |
| |
| Abstract: | This paper discusses a type of damped nonlinear Schr dinger equation with harmonic potential appearing in attractive Bose-Einstein condensates.With reference to the physical properties of Bose-Einstein condensates,we prove that there exists a threshold value for the damping parameter and when the damping parameter is above the threshold value, the solutions of the Cauchy problem globally exist;when the damping parameter is under the threshold value,the solutions will collapse in finite time. |
| |
| Keywords: | Bose-Einstein condensates Schr dinger equation harmonic potential damped Gross-Pitaevskii(GP)equation |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
