Japan Journal of Industrial and Applied Mathematics

, Volume 21, Issue 1, pp 75–108

Computer assisted proof to symmetry-breaking bifurcation phenomena in nonlinear vibration


DOI: 10.1007/BF03167433

Cite this article as:
Kawanago, T. Japan J. Indust. Appl. Math. (2004) 21: 75. doi:10.1007/BF03167433


Using the numerical verification method, we analyze a nonlinear vibration system with friction described by a wave equation related to the Duffing equation. We present a complete proof of the existence of a symmetry-breaking bifurcation point, which was first found in the numerical simulation. Our method is based on some general theorems established by the author in another paper [3] and is applicable to various systems described by semilinear partial differential equations including elliptic and parabolic ones. All of the numerical results in the proof can be accurately reproduced, though some of them are comparatively large scale. This reproducibility is realized by introducing a method for completely controlling the numerical calculations.

Key words

nonlinear vibrationbifurcationcomputer assisted proofalmost diagonal operatorcomplete reproducibility

Copyright information

© JJIAM Publishing Committee 2004

Authors and Affiliations

  1. 1.Department of MathematicsTokyo Institute of TechnologyTokyoJapan