| 带调和势的非线性Shr(o¨)dinger方程整体吸引子的维数估计 |
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| 引用本文： | 朱朝生.带调和势的非线性Shr(o¨)dinger方程整体吸引子的维数估计[J].西南师范大学学报(自然科学版),2005,30(5). |
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| 作者姓名： | 朱朝生 |
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| 作者单位： | 西南大学,数学与财经学院,重庆,400715 |
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| 摘 要： | 研究了带调和势的非线性Shr(o¨)dinger方程:iut+ uxx-x2u+|u|2u+iαu=f(x),α＞0的长时间动力学行为,给出了该方程整体吸引子的Hausdorff维数和Fractal维数的上界估计.
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| 关 键 词： | 非线性Shr(o¨)dinger方程 Hausdorff维数 Fractal维数 nonlinear Schr(o¨)dinger equation |
An Estimate of the Dimensions of the Global Attractor for the Nonlinear Schr(o¨)dinger Equation with Harmonic Potential |
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| ZHU Chao-sheng.An Estimate of the Dimensions of the Global Attractor for the Nonlinear Schr(o¨)dinger Equation with Harmonic Potential[J].Journal of Southwest China Normal University(Natural Science),2005,30(5). |
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| Authors: | ZHU Chao-sheng |
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| Abstract: | In this paper, the long time behavior of solution for the nonlinear Schr(o¨)dinger equation with harmonic po tential: iut + uxx - x2 u + |u| 2 u + iau = f ( x ) , a ＞ 0 is studied. The estimates of the upper bounds of Hausdorff and Fractal dimensions for the global attractors are obtained. |
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| Keywords: | Hausdorff dimensions Fractal dimensions |
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