Frontiers of Mathematics in China >
Almost periodic solutions for a class of higher dimensional Schrödinger equations
Received date: 06 Jun 2008
Accepted date: 11 Sep 2009
Published date: 05 Sep 2009
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In this paper, we show that there are almost periodic solutions corresponding to full dimensional invariant tori for higher dimensional Schröodinger 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.
Key words: Schrodinger equation; almost-periodic solution; KAM method
Jiansheng GENG . Almost periodic solutions for a class of higher dimensional Schrödinger equations[J]. Frontiers of Mathematics in China, 2009 , 4(3) : 463 -482 . DOI: 10.1007/s11464-009-0029-1
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