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

Wattis, Jonathan A.D.

Abstract

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.

Citation

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

• Journal Article Type: Article
• Acceptance Date: Feb 14, 2019
• Online Publication Date: Mar 14, 2019
• Publication Date: Mar 14, 2019
• Deposit Date: Feb 14, 2019
• Publicly Available Date: Mar 18, 2019
• Journal: Mathematics in Engineering
• Electronic ISSN: 2640-3501
• Publisher: AIMS Press
• Peer Reviewed: Peer Reviewed
• Volume: 1
• Issue: 2
• Pages: 327-342
• DOI: https://doi.org/10.3934/mine.2019.2.327
• Keywords: solitary travelling waves; lattice dynamics; diatomic; FPU; asymptotic analysis
• Public URL: https://nottingham-repository.worktribe.com/output/1549514
• Publisher URL: http://www.aimspress.com/article/10.3934/mine.2019.2.327