带有弱阻尼项的非线性Schrdinger方程全离散Fourier拟谱格式的长时间行为  

Long-time behavior of fully discrete Fourier pseudo-spectral scheme to nonlinear Schrdinger equation with weakly damped

作　　者：苏在滨[1] 张法勇[2,3] 范广慧[1] 

机构地区：[1]黑龙江工程学院数学系,哈尔滨150001 [2]黑龙江大学数学科学学院,哈尔滨150080 [3]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2010年第3期296-303,共8页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(10371077);黑龙江省教育厅面上项目(11521240)

摘　　要：针对带有弱阻尼项的非线性Schrdinger方程周期初值问题,研究一个全离散Fourier拟谱格式。基于对拟谱逼近解所做的一系列的一致先验估计,得到拟谱格式在[0,T]上按L2模的稳定性和拟谱逼近解最优的误差估计。最后证明由全离散Fourier拟谱格式生成的离散动力系统存在整体的吸引子。A fully discrete Fourier pseudo-spectral scheme to a nonlinear Schoedinger equation with weakly damped is analyzed. On the basis of a series of the time-uniform priori estimates of the pseudo-spectral approximate solutions, the stability of the fully discrete Fourier pseudo-spectral scheme and the error bounds of optimal order of the approximate solutions are obtained in L2-module over a finite time interval [ O, T]. Finally, the existence of a maximal attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.

关 键 词：带有弱阻尼项的非线性Schrdinger方程 FOURIER拟谱方法 无穷维动力系统 整体吸引子 

分 类 号：O175.13[理学—数学]