skip to main content

SciTech ConnectSciTech Connect

Title: Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies

Consider the one dimensional nonlinear beam equation u{sub tt} + u{sub xxxx} + mu + u{sup 3} = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form.‚ÄČ.
Authors:
 [1] ; ;  [2]
  1. College of Information Technology, Jilin Agricultural University, Changchun 130118 (China)
  2. School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024 (China)
Publication Date:
OSTI Identifier:
22403146
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 5; 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; BEAMS; DIRICHLET PROBLEM; EQUATIONS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; PERIODICITY