# American Institute of Mathematical Sciences

September  2011, 31(3): 997-1015. doi: 10.3934/dcds.2011.31.997

## Almost periodic solutions for a class of semilinear quantum harmonic oscillators

 1 Department of Mathematics, Nanjing University, Nanjing 210093, China, China

Received  June 2010 Revised  October 2010 Published  August 2011

In this paper, we show that there are many almost periodic solutions corresponding to full dimensional invariant tori for the semilinear quantum harmonic oscillators with Hermite multiplier $${\rm i}{u}_{t}-u_{xx}+x^2u + M_\xi u+\varepsilon |u|^{2m}u=0,\quad u\in C^1(\Bbb R,L^2(\Bbb R)),$$ where $m \geq 1$ is an integer. The proof is based on an abstract infinite dimensional KAM theorem.
Citation: Jian Wu, Jiansheng Geng. Almost periodic solutions for a class of semilinear quantum harmonic oscillators. Discrete & Continuous Dynamical Systems, 2011, 31 (3) : 997-1015. doi: 10.3934/dcds.2011.31.997
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