December  2006, 5(4): 839-853. doi: 10.3934/cpaa.2006.5.839

Quasi-periodic solutions for 1D resonant beam equation

1. 

School of Mathematical Sciences, Institute of Mathematics, Fudan University, Shanghai 200433, China

2. 

Department of Mathematics, Nanjing University, Nanjing 210093, China

Received  January 2006 Revised  June 2006 Published  September 2006

In this paper, one--dimensional ($1D$) resonant beam equation

$u_{t t} +u_{x x x x} +u^3=0,$

with hinged boundary conditions is considered. It is proved that the above equation admits small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system. The proof is based on infinite dimensional KAM theorem, partial normal form and scaling skills.

Citation: Zhenguo Liang, Jiansheng Geng. Quasi-periodic solutions for 1D resonant beam equation. Communications on Pure and Applied Analysis, 2006, 5 (4) : 839-853. doi: 10.3934/cpaa.2006.5.839
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