Soliton Canal

A shallow canal whose water surface obeys the Korteweg-de Vries equation, solved live by a real Fourier pseudo-spectral integrator. A soliton is a single smooth hump that travels at constant speed without spreading, because nonlinear steepening exactly cancels dispersive spreading. Taller solitons move faster (speed = twice amplitude), so a tall one launched behind a short one catches up, passes through it, and both emerge with their original shapes and only a shift in position. Launch your own by clicking the water; or pick the contrast preset where an ordinary lump, not a soliton, just fans out into ripples.