{"paper":{"title":"Linearizability of the Perturbed Burgers Equation","license":"","headline":"","cross_cats":["nlin.SI"],"primary_cat":"solv-int","authors_text":"Brazil), E. C. de Rey Neto (IFT-UNESP, J. G. Pereira, R. A. Kraenkel, Sao Paulo","submitted_at":"1997-03-19T14:38:15Z","abstract_excerpt":"We show in this letter that the perturbed Burgers equation $u_t = 2uu_x + u_{xx} + \\epsilon ( 3 \\alpha_1 u^2 u_x + 3\\alpha_2 uu_{xx} + 3\\alpha_3 u_x^2 + \\alpha_4 u_{xxx} )$ is equivalent, through a near-identity transformation and up to order \\epsilon, to a linearizable equation if the condition $3\\alpha_1 - 3\\alpha_3 - 3/2 \\alpha_2 + 3/2 \\alpha_4 = 0$ is satisfied. In the case this condition is not fulfilled, a normal form for the equation under consideration is given. Then, to illustrate our results, we make a linearizability analysis of the equations governing the dynamics of a one-dimensio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"solv-int/9703009","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"}