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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.<\/jats:p>","DOI":"10.1137\/16m108639x","type":"journal-article","created":{"date-parts":[[2018,4,19]],"date-time":"2018-04-19T12:05:38Z","timestamp":1524139538000},"page":"1182-1212","source":"Crossref","is-referenced-by-count":26,"title":["Nanoptera in a Period-2 Toda Chain"],"prefix":"10.1137","volume":"17","author":[{"given":"Christopher J.","family":"Lustri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mason A.","family":"Porter","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,4,19]]},"reference":[{"key":"atypb1","unstructured":"NIST Digital Library of Mathematical Functions\n                      , release 1.0.10, National Institute of Standards and Technology,http:\/\/dlmf.nist.gov\/(2015)."},{"key":"atypb2","unstructured":"M. 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