Solitary wave
= Solitary wave
{title2=$u(x,t)=U(x-ct),\quad U(\xi)\to0\text{ as }|\xi|\to\infty$}
A solitary wave is a spatially localized <travelling wave> that retains its profile as it propagates. The displayed form uses a zero background; other constant backgrounds are possible. A <soliton> additionally has the characteristic elastic interaction property with other solitons. The existence of a single localized travelling profile does not alone establish that stronger property.