Asymptotic approximations to travelling waves in the diatomic Fermi-Pasta-Ulam lattice

Jonathan A. D. Wattis; Jonathan A. D. Wattis

doi:10.3934/mine.2019.2.327

Mathematics in Engineering

2019, Volume 1, Issue 2: 327-342. doi: 10.3934/mine.2019.2.327

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Asymptotic approximations to travelling waves in the diatomic Fermi-Pasta-Ulam lattice

Jonathan A. D. Wattis ^,

School of Mathematical Sciences,University of Nottingham,University Park,Nottingham,NG7 2RD,UK

Received: 23 November 2018 Accepted: 14 February 2019 Published: 14 March 2019

We construct high-order approximate travelling waves solutions of the diatomic Fermi-Pasta-Ulam lattice using asymptotic techniques which are valid for arbitrary mass ratios. Separately small amplitude ansatzs are made for the motion of the lighter and heavier particles, which are coupled The Fredholm alternative is used to derive consistency conditions, whose solution generates small amplitude expansions for both sets of particles.

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Citation: Jonathan A. D. Wattis. Asymptotic approximations to travelling waves in the diatomic Fermi-Pasta-Ulam lattice[J]. Mathematics in Engineering, 2019, 1(2): 327-342. doi: 10.3934/mine.2019.2.327

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Abstract

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