The Mathematics of the Mexican Wave

A Mexican wave (la ola) is a stadium phenomenon where spectators stand and sit in sequence. It can be modelled as a wave on a ring: a travelling wave solution of the Kuramoto model (coupled oscillators). The wave speed depends on reaction time and the spread of influence. The wave is a soliton‑like structure: it maintains its shape and travels around the stadium. The mathematics is similar to neural firing in the brain (synaptic waves) and the spread of excitement in crowds. It shows how local interactions can create global patterns.