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

School of Mathematical Sciences,University of Nottingham,University Park,Nottingham,NG7 2RD,UK
$^\dagger$ This contribution is part of the Special Issue: Hamiltonian Lattice Dynamics
  Guest Editors: Simone Paleari; Tiziano Penati
  Link: http://www.aimspress.com/newsinfo/1165.html

Special Issues: Hamiltonian Lattice Dynamics

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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Keywords solitary travelling waves; lattice dynamics; diatomic; FPU; asymptotic analysis

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


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