{"paper":{"title":"General solutions of the Monge-Amp\\`{e}re equation in $n$-dimensional space","license":"","headline":"","cross_cats":["math.AP","nlin.SI","solv-int"],"primary_cat":"hep-th","authors_text":"A. N. Leznov, D. B. Fairlie","submitted_at":"1994-03-22T16:59:09Z","abstract_excerpt":"It is shown that the general solution of a homogeneous Monge-Amp\\`{e}re equation in $n$-dimensional space is closely connected with the exactly (but only implicitly) integrable system\n  \\frac {\\partial \\xi_{j}}{\\partial x_0}+\\sum_{k=1}^{n-1} \\xi_{k} \\frac {\\partial \\xi_{j}}{\\partial x_{k}}=0 \\label{1}\n  Using the explicit form of solution of this system it is possible to construct the general solution of the Monge-Amp\\`{e}re equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9403134","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"}