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Title: Quasi-periodic solutions for d-dimensional beam equation with derivative nonlinear perturbation

In this paper, we consider the d-dimensional beam equation with convolution potential under periodic boundary conditions. We will apply the Kolmogorov-Arnold-Moser theorem in Eliasson and Kuksin [Ann. Math. 172, 371-435 (2010)] into this system and obtain that for sufficiently small ε, there is a large subset S′ of S such that for all s ∈ S′, the solution u of the unperturbed system persists as a time-quasi-periodic solution which has all Lyapunov exponents equal to zero and whose linearized equation is reducible to constant coefficients.
Authors:
 [1] ;  [2]
  1. Department of Mathematics, Binzhou University, Shandong 256600 (China)
  2. School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024 (China)
Publication Date:
OSTI Identifier:
22479580
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 7; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; EQUATIONS; LYAPUNOV METHOD; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PERIODICITY; PERTURBATION THEORY; POTENTIALS