Traveling wave

Summary

A traveling wave is a solution of an evolution equation that moves at constant speed without changing its shape. In one space dimension it has the form $u(x, t) = U(x - ct)$, with a profile $U$ and a speed $c$. Substituting this form turns the partial differential equation into an ordinary differential equation for $U$. Traveling waves describe fronts in reaction–diffusion equations, viscous shock profiles and solitons. See the definition.