Response solution to complex Ginzburg–Landau equation with quasi-periodic forcing of Liouvillean frequency

Abstract

In this paper, the existence of a response solution with the Liouvillean frequency vector to the quasi-periodically forced complex Ginzburg–Landau equation, whose linearized system is elliptic–hyperbolic, is obtained. The proof is based on constructing a modified KAM theorem for an infinite-dimensional dissipative system with Liouvillean forcing frequency.