2010/03/08 by Roman O. Popovych, Artur Sergyeyev · 34 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Applied mathematics #Conservation law #Differential equation #Discrete mathematics #Geometry #Independent equation #Korteweg–de Vries equation #Law #Mathematical analysis #Mathematics #Modulo #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Order (exchange) #Partial differential equation #Physics #Political science #Quadratic equation #Simultaneous equations #Variable (mathematics) #math-ph #math.AP #math.MP #msc:35A30 #msc:35K55 #msc:37K05 #msc:37K35 #nlin.SI
paper · pdf · doi:10.1016/j.physleta.2010.03.033
published in Physics Letters A 374(22), 2210-2217 (Elsevier BV) · 16 pages
arxiv created 2010/03/08 · openalex publication_date 2010/03/18 · arxiv updated 2010/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study local conservation laws for evolution equations in two independent variables. In particular, we present normal forms for the equations admitting one or two low-order conservation laws. Examples include Harry Dym equation, Korteweg-de-Vries-type equations, and Schwarzian KdV equation. It is also shown that for linear evolution equations all their conservation laws are (modulo trivial conserved vectors) at most quadratic in the dependent variable and its derivatives.