Nanoptera in a period-2 Toda chain

Christopher J. Lustri, Mason Porter

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    We study asymptotic solutions to a singularly perturbed, period-2 Toda lattice and use exponential asymptotics to examine "nanoptera," which are nonlocal solitary waves with constant-amplitude, exponentially small wave trains. With this approach, we isolate the exponentially small, constant-amplitude waves, and we elucidate the dynamics of these waves in terms of the Stokes phenomenon. We find a simple asymptotic expression for these waves, and we study configurations in which these waves vanish, producing localized solitary-wave solutions. In the limit of small mass ratio between the two types of particles in the lattice, we derive a simple antiresonance condition for the manifestation of such solutions.
    Original languageEnglish
    Pages (from-to)1182–1212
    Number of pages31
    JournalSIAM Journal on Applied Dynamical Systems
    Volume17
    Issue number2
    DOIs
    Publication statusPublished - 19 Apr 2018

    Keywords

    • solitary waves
    • exponential asymptotics
    • nanoptera
    • Toda lattice

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