ALMOST PERIODIC SOLUTIONS FOR A CLASS OF SEMILINEAR QUANTUM HARMONIC OSCILLATORS

作者：Wu Jian^*; Geng Jiansheng

来源：Discrete and Continuous Dynamical Systems, 2011, 31(3): 997-1015.

DOI：10.3934/dcds.2011.31.997

• Almost periodic solutions
• KAM theory
• Quantum harmonic oscillators

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
iu(t) - u(xx) + x(2)u + M xi u + epsilon vertical bar u vertical bar(2m) u = 0; u is an element of C(1)(R, L(2) (R)),
where m >= 1 is an integer. The proof is based on an abstract in finite dimensional KAM theorem.

• 出版日期2011-11
• 单位南京大学