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 language | English |
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Pages (from-to) | 1182–1212 |
Number of pages | 31 |
Journal | SIAM Journal on Applied Dynamical Systems |
Volume | 17 |
Issue number | 2 |
DOIs | |
Publication status | Published - 19 Apr 2018 |
Keywords
- solitary waves
- exponential asymptotics
- nanoptera
- Toda lattice