Shock waves in the Toda lattice: Analysis

Brad Lee Holian, Hermann Flaschka, David W. McLaughlin

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


Known analytical results are used to analyze molecular-dynamics experiments of shock waves in the one-dimensional Toda lattice. (This lattice provides a physically realistic model which contains the hard-sphere and harmonic lattices as limits.) Both explicit solutions and rather general theoretical properties have been employed. The leading edge of the shock front is well represented quantitatively by a single isolated solition. Once compression is properly taken into account, the interior of the shock wave is accurately described by a slowly varying Toda wave train. A sharp transition in the dynamical response exists as the shock strength passes a critical value; this critical value is identified mathematically by the spectral transform for the Toda lattice. Finally, a local spectral transform is used to measure, directly from the numerical data, the wave-train characteristics of the shock profile.

Original languageEnglish (US)
Pages (from-to)2595-2623
Number of pages29
JournalPhysical Review A
Issue number5
StatePublished - 1981

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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