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Appl. Math."],"published-print":{"date-parts":[[2026,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In the present work we study discrete nonlinear Schr\u00f6dinger models combining nearest neighbor (NN) and next-nearest neighbor (NNN) interactions, motivated by experiments in waveguide arrays. We consider both the more experimentally accessible case of positive ratio [Formula: see text] of NNN to NN interactions, as well as the intriguing case of competing such interactions [Formula: see text], where stationary states can exist only for [Formula: see text]. We analyze the key eigenvalues for the stability of the pulse-like stationary (ground) states, and find that such modes depend exponentially on the coupling parameter [Formula: see text], with suitable polynomial prefactors and corrections that we analyze in detail. Very good agreement of the resulting predictions is found with systematic numerical computations of the associated eigenvalues. This analysis uses Borel\u2013Pad\u00e9 exponential asymptotics to determine Stokes multipliers in the solution; these multipliers cannot be obtained using standard matched asymptotic expansion approaches as they are hidden beyond all asymptotic orders, even near singular points. By using Borel\u2013Pad\u00e9 methods near the singularity, we construct a general asymptotic template for studying parametric problems which require the calculation of subdominant Stokes multipliers.<\/jats:p>","DOI":"10.1137\/25m177028x","type":"journal-article","created":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T08:02:11Z","timestamp":1782979331000},"page":"1504-1526","source":"Crossref","is-referenced-by-count":0,"title":["Borel\u2013Pad\u00e9 Exponential Asymptotics for the Discrete Nonlinear Schr\u00f6dinger Model with Next-to-Nearest Neighbor Interactions"],"prefix":"10.1137","volume":"86","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9504-277X","authenticated-orcid":true,"given":"Christopher J.","family":"Lustri","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, University of Sydney, Camperdown 2050, Australia."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"In\u00eas","family":"Aniceto","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, UK."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7714-3689","authenticated-orcid":true,"given":"P. G.","family":"Kevrekidis","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003 USA, and Department of Physics, University of Massachusetts Amherst, Amherst, MA 01003 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,7,2]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2022.133440"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1111\/sapm.70119"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2019.02.003"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP02(2019)073"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.4310\/CNTP.2012.v6.n2.a3"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1142\/S0217984904007190"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2007.03.003"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1998.0278"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-77884-6"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1140\/epjs\/s11734-021-00267-x"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1111\/sapm.12660"},{"key":"ref12","unstructured":"R. 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