{"paper":{"title":"Particular solutions to multidimensional PDEs represented in the form of one-dimensional flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"A. I. Zenchuk","submitted_at":"2013-09-20T04:48:21Z","abstract_excerpt":"We represent an algorithm reducing the $(M+1)$-dimensional nonlinear partial differential equation (PDE) representable in the form of one-dimensional flow $u_t + w_{x_1}(u,u_{x},u_{xx},\\dots)=0$, (where $w$ is an arbitrary local function of $u$ and its $x_i$-derivatives, $i=1,\\dots,M$) to the family of $M$-dimensional nonlinear PDEs $F(u,w)=0$, where $F$ is general (or particular) solution of a certain second order two-dimensional nonlinear PDE. Particularly, the $M$-dimensional PDE might be an ODE which, in some cases, may be integrated yielding the explicite solutions to the original ($M+1$)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5171","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"}