{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:29:17Z","timestamp":1787232557298,"version":"build-2736575974"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>We demonstrate existence of waves localized at the interface of two nonlinear periodic media with different coefficients of the cubic nonlinearity via the one-dimensional Gross\u2013Pitaevsky equation. We call these waves the surface gap solitons (SGSs). In the case of smooth symmetric periodic potentials, we study analytically bifurcations of SGSs from standard gap solitons and determine numerically the maximal jump of the nonlinearity coefficient allowing for SGS existence. We show that the maximal jump vanishes near the thresholds of bifurcations of gap solitons. In the case of continuous potentials with a jump in the first derivative at the interface, we develop a homotopy method of continuation of SGS families from the solution obtained via gluing of parts of the standard gap solitons and study existence of SGSs in the photonic band gaps. We explain the termination of the SGS families in the interior points of the band gaps from the bifurcation of linear bound states in continuous nonsmooth potentials.<\/jats:p>","DOI":"10.1137\/060676751","type":"journal-article","created":{"date-parts":[[2008,4,23]],"date-time":"2008-04-23T18:23:16Z","timestamp":1208974996000},"page":"249-264","source":"Crossref","is-referenced-by-count":10,"title":["Surface Gap Solitons at a Nonlinearity Interface"],"prefix":"10.1137","volume":"7","author":[{"given":"Tom\u00e1\u0161","family":"Dohnal","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dmitry","family":"Pelinovsky","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,4,23]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1364\/OE.14.002151"},{"key":"R2","unstructured":"M. S. Eastham,\n                      The Spectral Theory of Periodic Differential Equations\n                      , Scottish Academic Press, Edinburgh, 1973."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2006.03.009"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1364\/OPEX.13.007720"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1364\/OE.14.004049"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1364\/OL.31.002172"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.96.073901"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.115.809"},{"key":"R9","unstructured":"W. Magnus and S. Winkler,\n                      Hill's Equation\n                      , Interscience Tracts in Pure and Applied Mathematics 20, John Wiley & Sons, New York, London, Sydney, 1966."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1364\/OL.30.002466"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1007\/s00032-005-0047-8"},{"key":"R12","doi-asserted-by":"crossref","unstructured":"D. Pelinovsky,\n                      Asymptotic reductions of the Gross\u2013Pitaevskii equation\n                      , in Emergent Nonlinear Phenomena in Bose\u2013Einstein Condensates: Theory and Experiment, P. Kevrekidis, D. Frantzeskakis, and R. Carretero, eds., Springer-Verlag, Heidelberg, 2007, pp. 377\u2013398.","DOI":"10.1007\/978-3-540-73591-5_19"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.70.036618"},{"key":"R14","unstructured":"B. Simon and M. Reed,\n                      Methods of Modern Mathematical Physics\n                      IV:\n                      Analysis of Operators\n                      , Academic Press, New York, 1978."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.97.193902"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.96.063901"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1364\/OL.5.000323"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.76.013621"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060676751","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:03:49Z","timestamp":1787231029000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060676751"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/060676751"],"URL":"https:\/\/doi.org\/10.1137\/060676751","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}