Nonlinear normal modes for the Toda Chain

W. E. Ferguson, H. Flaschka, D. W. McLaughlin

Research output: Contribution to journalArticlepeer-review


The Toda Chain is a nonlinear mass-spring chain which can in principle be integrated analytically by the action-angle theory of classical mechanics. We show that the transformation from physical variables to action variables can be implemented very simply on a computer. We study the correspondence between action variables and the motions of the chain, and find the role of the action variables to be very similar to the role of normal-mode amplitudes in the harmonic chain. This similarity leads to a partly rigorous, partly heuristic normal-mode analysis for the Toda chain. New results are obtained when this normal-mode analysis is applied to certain perturbations of the Toda chain such as the Fermi-Pasta-Ulam chain or the Toda chain with a mass impurity.

Original languageEnglish (US)
Pages (from-to)157-209
Number of pages53
JournalJournal of Computational Physics
Issue number2
StatePublished - Feb 1982

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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