{"paper":{"title":"On transverse stability of discrete line solitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Dmitry E. Pelinovsky, Jianke Yang","submitted_at":"2012-10-02T21:55:31Z","abstract_excerpt":"We obtain sharp criteria for transverse stability and instability of line solitons in the discrete nonlinear Schr\\\"{o}dinger equations on one- and two-dimensional lattices near the anti-continuum limit. On a two-dimensional lattice, the fundamental line soliton is proved to be transversely stable (unstable) when it bifurcates from the $X$ ($\\Gamma$) point of the dispersion surface. On a one-dimensional (stripe) lattice, the fundamental line soliton is proved to be transversely unstable for both signs of transverse dispersion. If this transverse dispersion has the opposite sign to the discrete "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0938","kind":"arxiv","version":1},"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"}