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中文摘要：
对非线性Schrodinger-Boussinesq方程的初边值问题,一般采用有限差分方法在空间方向离散该方程,已经得到了近似解的误差估计,证明了近似吸引子的存在性和上半连续性。在此基础之上,进一步研究带弱阻尼的非线性Schrodinger-Boussinesq方程有限差分解近似吸引子的几何结构,证明近似吸引子的Hausdorff和分形维数是有限的。
英文摘要：
In previous research paper, the initial-boundary value problem of nonlinear Schrodinger- Boussinesq equation with weak damping is discretized by employing finite difference method in spatial di- rection. The error estimate of the approximate solution has been obtained and the existence of the approxi- mate attractor and its upper semicontinuity have been proved. On this basis, geometrical structure of the approximate attractor for finite difference solution of nonlinear Schodinger-Boussinesq equations with weak damping is further investigated. It is proved that the Hausdorff and fractal dimensions of the approximate attractor are finite.
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