1999/09/15 by Sung Ho Wang, Wang, Sung Ho
Mathematics · Medicine · #35K22 #35L65 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #math.AP #math.DG #msc:35K22 #msc:35L65
paper · pdf · doi:10.48550/arxiv.math/9909086
27 pages
arxiv created 1999/09/15 · openalex publication_date 1999/09/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation law has a unique representative. The structure of this subspace naturally gives rise to the convenient notion of the weight of a conservation law, and we also compute a universal integrability condition to admit any higher order (weight) conservation law. As an example, the differential system descrbing the flow of the curve in the plane by the derivative of its curvature with respect to the arclength is shown to have the KdV property, i.e., an infinite sequence of conservation laws of distnct weights.