Long-time behaviour for Hirota equation

Abstract

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.