KAM Tori for Higher Dimensional Quintic Beam Equation

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Abstract

In this paper, we consider higher dimensional quintic beam equation
$$\begin{aligned} u_{tt} +\triangle ^2 u+u+u^5 =0, \end{aligned}$$
with periodic boundary conditions, it is proved that the above equation admits a family of small-amplitude linearly stable quasi-periodic solutions.

Keywords

Beam equation KAM Tori Birkhoff normal form 

Mathematics Subject Classification

Primary 37K60 37K55 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsNanjing UniversityNanjingPeople’s Republic of China

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