{"paper":{"title":"Spectral parameter power series representation for solutions of linear system of two first order differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.NA"],"primary_cat":"math.CA","authors_text":"Nelson Guti\\'errez Jim\\'enez, Sergii M. Torba","submitted_at":"2019-04-06T05:07:26Z","abstract_excerpt":"A representation in the form of spectral parameter power series (SPPS) is given for a general solution of a one dimension Dirac system containing arbitrary matrix coefficient at the spectral parameter, \\[ B \\frac{dY}{dx} + P(x)Y = \\lambda R(x)Y,\\] where $Y=(y_1,y_2)^T$ is the unknown vector-function, $\\lambda$ is the spectral parameter, $B = \\begin{pmatrix}0 & 1 \\\\ -1 & 0\\end{pmatrix}$, and $P$ is a symmetric $2\\times 2$ matrix, $R$ is an arbitrary $2\\times 2$ matrix whose entries are integrable complex-valued functions. The coefficient functions in these series are obtained by recursively ite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03361","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"}