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Almost periodic solutions for a class of higher dimensional Schr?dinger equations |
Jiansheng GENG( ) |
| Department of Mathematics and Institute of Mathematical Science, Nanjing University, Nanjing 210093, China |
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Abstract In this paper, we show that there are almost periodic solutions corresponding to full dimensional invariant tori for higher dimensional Schr?odinger equations with Fourier multiplier iut-Δu+Mξu+f(|u|2)u = 0, subject to periodic boundary conditions, where the nonlinearity f is a realanalytic function near u = 0 with f(0) = 0.The proof is based on an improved infinite dimensional KAM theorem.
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| Keywords
Schrodinger equation
almost-periodic solution
KAM method
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Corresponding Author(s):
GENG Jiansheng,Email:jgeng@nju.edu.cn
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Issue Date: 05 September 2009
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