{"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). 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.4858","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}