Time-averaging for weakly nonlinear CGL equations with arbitrary potentials

Guan Huang, Sergei Kuksin, Alberto Maiocchi

Consider weakly nonlinear complex Ginzburg--Landau (CGL) equation of the form: $$u_t+i(-\Delta u+V(x)u)=\epsilon \mu \Delta u+\epsilon \mathcal{P}(u),x\in R^d,(\ast )$$ under the periodic boundary…