{"paper":{"title":"Heat operator with pure soliton potential: properties of Jost and dual Jost solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"A. Pogrebkov, F. Pempinelli, M. Boiti","submitted_at":"2011-05-18T16:29:42Z","abstract_excerpt":"Properties of Jost and dual Jost solutions of the heat equation, $\\Phi(x,k)$ and $\\Psi(x,k)$, in the case of a pure solitonic potential are studied in detail. We describe their analytical properties on the spectral parameter $k$ and their asymptotic behavior on the $x$-plane and we show that the values of $e^{-qx}\\Phi(x,k)$ and the residua of $e^{qx}\\Psi(x,k)$ at special discrete values of $k$ are bounded functions of $x$ in a polygonal region of the $q$-plane. Correspondingly, we deduce that the extended version $L(q)$ of the heat operator with a pure solitonic potential has left and right an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3681","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"}