We investigate the long time behavior of the damped, forced KdV-BO equation driven by white noise. We first show that the global solution generates a random dynamical system. By energy type estimates and dispersive properties, we then prove that this system possesses a weak random attractor in the space .
Guolian Wang. "A Stochastic Weakly Damped, Forced KdV-BO Equation." Abstr. Appl. Anal. 2014 (SI66) 1 - 8, 2014. https://doi.org/10.1155/2014/576087