# American Institute of Mathematical Sciences

August  2017, 22(6): 2501-2519. doi: 10.3934/dcdsb.2017104

## Quasi-periodic solutions of generalized Boussinesq equation with quasi-periodic forcing

 1 College of Mathematics and Physics, Yancheng Institute of Technology, Yancheng 224051, China 2 Department of Mathematics, Southeast University, Nanjing 211189, China

Received  August 2014 Revised  November 2015 Published  March 2017

Fund Project: This work is supported by the Tian Yuan special Funds of the National Natural Science Foundation of China (Grant No. 11526178), NSFJS Grant (BK 20131285) and NSFC Grant(11371090,11301072)

In this paper, one-dimensional quasi-periodically forced generalized Boussinesq equation
 $u_{tt}-u_{xx} + u_{xxxx} +\varepsilon \phi(t) ( u+u^3 )_{xx}=0$
with hinged boundary conditions is considered, where
 $\varepsilon$
is a small positive parameter,
 $\phi(t)$
is a real analytic quasi-periodic function in
 $t$
with frequency vector
 $\omega=( \omega_1,\omega_2,\cdots,\omega_m ).$
It is proved that, under a suitable hypothesis on
 $\phi(t),$
there are many quasi-periodic solutions for the above equation via KAM theory.
Citation: Yanling Shi, Junxiang Xu, Xindong Xu. Quasi-periodic solutions of generalized Boussinesq equation with quasi-periodic forcing. Discrete & Continuous Dynamical Systems - B, 2017, 22 (6) : 2501-2519. doi: 10.3934/dcdsb.2017104
##### References:

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