Khasminskii--Whitham averaging for randomly perturbed KdV equation

Sergei B. Kuksin, Andrey L. Piatnitski

We consider the damped-driven KdV equation $$\dot{u}-\nu u_{xx}+u_{xxx}-6u{u}_x=\sqrt{\nu }\eta (t,x),x\in S^1,\int udx\equiv \int \eta dx\equiv 0,$$ where $0<\nu \le 1$ and the random process $\eta$ i…