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arXiv · 1607.07065

Nanoptera in a Period-2 Toda Chain

Christopher J. Lustri·Mason A. Porter
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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 the waves, and we study configurations in which these waves vanish, producing localized solitary-wave solutions. In the limit of small mass ratio, we derive a simple anti-resonance condition for the manifestation these wave-free solutions.

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Christopher J. Lustri, Mason A. Porter. 2016-07-24. Nanoptera in a Period-2 Toda Chain. https://doi.org/10.1137/16m108639x

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