{"paper":{"title":"A New Graded Algebra Structure on Differential Polynomials: Level Grading and its Application to the Classification of Scalar Evolution Equations in 1+1 Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"A. H. Bilge, E. Mizrahi","submitted_at":"2012-04-14T13:32:50Z","abstract_excerpt":"We define a new grading, that we call the \"level grading\", on the algebra of polynomials generated by the derivatives $u_{k+i}=\\partial^{k+i}u/\\partial x^{k+i}$ over the ring $K^{(k)}$ of $C^{\\infty}$ functions of $u,u_1,...,u_k$. This grading has the property that the total derivative and the integration by parts with respect to $x$ are filtered algebra maps. In addition, if $u$ satisfies an evolution equation $u_t=F[u]$ and $F$ is a level homogeneous differential polynomial, then the total derivative with respect to $t$, $D_t$, is also a filtered algebra map. Furthermore if $\\rho$ is level h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3171","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"}