{"paper":{"title":"Inverse Problem of Diffraction by an Inhomogeneous Solid with a Piecewise Hoelder Refractive Index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Aleksei Tsupak, Mikhail Medvedik, Yury Smirnov","submitted_at":"2018-03-13T09:39:03Z","abstract_excerpt":"The problem of reconstruction of an unknown refractive index $k(x)$ of an inhomogeneous solid $P$ is considered. The refractive index is assumed to be a piecewise-H\\\"{o}lder function\n  The original boundary value problem for the Helmholtz equation is reduced to the integral Lippman-Schwinger equation. The incident wave is defeined by a point source located outside $P.$ The solution of the inverse problem is obtained in two steps. First, the \"current\" $ J = (k^2 - k_0^2)u$ is determined in the inhomogeneity region. Second, the desired function $k (x) $ is expressed via the current $ J (x) $ and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04701","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"}