On the quasi-periodic solutions for generalized Boussinesq equation with higher order nonlinearity

Abstract

In this paper, one-dimensional generalized Boussinesq equation with hinged boundary conditions is considered, where . It is proved that for each prescribed integer , the above equation admits a Whitney-smooth family of small amplitude, quasi-periodic solutions with -dimensional Diophantine frequencies. The proof is based on an infinite-dimensional KAM theorem, partial Birkhoff normal form and scaling skills.

Keywords:

• generalized Boussinesq equation
• KAM theorem
• invariant tori
• infinite dimensional Hamiltonian system

MSC:

• 37K55
• 37N10
• 35Q35

Acknowledgements

The authors thank the editor and the referees for several kinds of suggestions.

Notes

This work was supported by NSFJS [BK 20131285], the Scientific Research and Innovation Project for College postgraduates in Jiangsu, China [cxzz12-0083], the NSFC [11371090] and the NSFC [11301072].