{"paper":{"title":"Linear stability analysis for traveling waves of second order in time PDE's","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Atanas Stefanov, Milena Stanislavova","submitted_at":"2011-08-11T14:31:45Z","abstract_excerpt":"We develop a general theory for linear stability of traveling waves of second order in time PDE's. More precisely, we introduce an explicitly computable index $\\om^*\\in (0, \\infty]$ (depending on the self-adjoint part of the linearized operator) so that the wave is stable if and only if $|c|\\geq \\om^*$. The results are applicable both in the periodic case and in the whole line case. As an application, we consider three classical models - the Boussinesq equation, the Klein-Gordon-Zakharov (KGZ) system and the fourth order beam equation. For the Boussinesq model and the KGZ system (and as a dire"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2417","kind":"arxiv","version":2},"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"}