Global Classification of Two-Component Approximately Integrable Evolution Equations

Abstract

We globally classify two-component evolution equations, with homogeneous diagonal linear part, admitting infinitely many approximate symmetries. Important ingredients are the symbolic calculus of Gel’fand and Dikiĭ, the Skolem–Mahler–Lech theorem, an algorithm of Smyth, and results on diophantine equations in roots of unity obtained by Beukers.