## Long-time behaviour for Hirota equation## Xianyun Guo, Chaosheng Zhu
In this paper, we investigate the long-time behavior of the solutions for the Hirota equation with the periodic
boundary condition. At first, by time uniform priori estimates of
solutions, we obtain the existence of global solutions. Furthermore, we prove the existence of a global attractor.
Finally, by squeezing property and Lipschitz continuity, we prove the existence of an exponential attractor of finite
fractal dimension which contains the global attractor.
Tbilisi Mathematical Journal, Vol. 5(1) (2012), pp. 51-64 |