Abstract
We extend our previous analysis of vibrational propagation in a chain of nonlinear oscillators to obtain explicit expressions for oscillator displacements and mean-squaredisplacements of the vibrational excitation for optical dispersion and study the effects of the interplay of initial conditions with nonlinearity.
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The functionF(x/k) can be evaluated in terms of elliptic integrals of first kind and second kind. See, e.g., Gradshteyn, I.S., Ryzhik, I.M.: Table of integrals, series, and products. Jeffrey, A. (ed.), p. 164. New York: Academic Press 1980
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Fan, X., Kenkre, V.M. A model calculation for vibrational propagation in a chain of nonlinear oscillators II: Effects of optical dispersion and of initial conditions. Z. Physik B - Condensed Matter 77, 425–429 (1989). https://doi.org/10.1007/BF01453793
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DOI: https://doi.org/10.1007/BF01453793