On the Classification of Scalar Non-Polynomial Evolution Equations: Quasilinearity

2004/03/17 by Ayşe Hümeyra Bilge, Ayse Humeyra Bilge, Bilge, Ayse Humeyra
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Waves and Solitons #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0403034

15 pages, no figures

arxiv created 2004/03/17 · openalex publication_date 2004/03/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that, for m≥ 7, scalar evolution equations of the form u_t=F(x,t,u,...,u_m) which admit a nontrivial conserved density of order m+1 are linear in u_m. The existence of such conserved densities is a necesary condition for integrability in the sense of admitting a formal symmetry, hence integrable scalar evolution equations of order m≥ 7 are quasilinear.

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