Global Attractor for the Generalized Dissipative KDV Equation with Nonlinearity

In order to study the longtime behavior of a dissipative evolutionary equation, we generally aim to show that the dynamics of the equation is finite dimensional for long time. In fact, one possible way to express this fact is to prove that dynamical systems describing the evolutional equation comprise the existence of the global attractor 1 . The KDV equation without dissipative and forcing was initially derived as a model for one direction water waves of small amplitude in shallow water, and it was later shown to model a number of other physical stems. In recent years, the KDV equations has been always being an important nonlinear model associated with the science of solids, liquids, and gases from different perspectives both mathematics and physics. As for dissipative KDV equation, existence of a global attractor is a significant feature. In 2 , Ghidaglia proved that for the dissipative KDV equation