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We compute families of 1D SGSs using the arclength continuation method for a range of values of the jump in $\\Gamma$. Using asymptotics, we show that when the frequency parameter converges to the bifurcation gap edge, the size of the allowed jump in $\\Gamma$ converges to 0 for SGSs centered at any $x_c\\in \\R$.\n  Linear stability of SGSs is ne"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0910.4858","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2009-10-26T11:49:54Z","cross_cats_sorted":["math.DS","math.SP","physics.optics"],"title_canon_sha256":"40efca38c792a0e79a5cc1a7a5771a9f070dabe31a4ed8b57be070824ccea952","abstract_canon_sha256":"177073f564e1acb11887c930b6856a1fff0592dd585aacfda3073b32855cff3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:47.838775Z","signature_b64":"ClZHhUa4OewUIyNF423tM0qGSDCEZuNz2aE5BHt0qfnJ2//7Vp74lEVQ/avEDaZIxz5Ch/ElG/8MkK2arpwCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6d959b0c04cca92328c6fa232c18f3975d485761d59f37ee940a31c8a3ef418","last_reissued_at":"2026-05-18T04:27:47.838254Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:47.838254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Families of Surface Gap Solitons and their Stability via the Numerical Evans Function Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.SP","physics.optics"],"primary_cat":"nlin.PS","authors_text":"Elizabeth Blank, Tom\\'a\\v{s} Dohnal","submitted_at":"2009-10-26T11:49:54Z","abstract_excerpt":"The nonlinear Schr\\\"{o}dinger equation with a linear periodic potential and a nonlinearity coefficient $\\Gamma$ with a discontinuity supports stationary localized solitary waves with frequencies inside spectral gaps, so called surface gap solitons (SGSs). 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