Quasi‐periodic traveling waves for a class of damped beams on rectangular tori

Abstract

This article concerns a class of beam equations with damping on rectangular tori. When the generators satisfy certain relationship, by excluding some values of two model parameters, we prove that such models admit small amplitude quasi‐periodic traveling wave solutions with two frequencies, which are continuations of two rotating wave solutions with one frequency. The result holds not only for a rational torus but also for an irrational one. The proof is mainly based on a Lyapunov–Schmidt reduction together with the implicit function theorem.