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 Dikiǐ, the Skolem-Mahler-Lech theorem, an algorithm of Smyth, and results on diophantine equations in roots of unity obtained by Beukers.
Funding
This research has been funded by the Australian Research Council through the Centre of Excellence for Mathematics and Statistics of Complex Systems.