Dynamics of nonlinear mass-spring chains near the continuum limit

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Abstract

We study the dynamics of mass-spring chains with arbitrary interparticle and substrate potentials and describe a systematic approach to derive the equations of motion near the continuum limit. Our method, which applies both to strictly one-dimensional problems and to one-dimensional chains free to move in three dimensions, correctly captures all terms to given order in discreteness and allows us to formulate well-behaved nonlinear partial differential equations for these systems. We re-examine the familiar cases of the Fermi-Pasta-Ulam problem and the Frenkel-Kontorova model and obtain new insights into these problems.

Original languageEnglish
Pages (from-to)222-227
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume118
Issue number5
DOIs
StatePublished - 20 Oct 1986
Externally publishedYes

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