Peregrine SolitonOut on open water almost every wave rises and falls with its neighbours — until, rarely, one doesn't. It grows to three times the surrounding height from perfectly calm water, and then closes back over itself as if nothing happened. This is the exact mathematical shape of that freak wave, replayed here as a glowing waterline that breathes in and out of a dark, calm sea.The nonlinear Schrödinger equation governs slowly-varying wave envelopes in deep water and optical fibres. It has a family of “breather” solutions — Kuznetsov–Ma breathers repeat in time, Akhmediev breathers repeat in space. Push either family's period to infinity and both collapse onto one doubly-localised pulse: the Peregrine soliton, predicted by Peregrine in 1983 and finally photographed in an optical fibre by Kibler et al. in 2010.