It was studied by Korteweg and de Vries late in the 19th century as a water wave equation, and after a long period of sleep, revived as one of the most fundamental equation of soliton phenomena.
Solitons emerge as peeks of the solution.
They will soon merge, and soon separate again. Here is an animation of such a numerical solution. The equation is solved under a periodic boundary condition. The initial value is a sinusoidal wave with one period over the whole space. The numerical solution shows that the sinusoidal wave soon developes into a train of solitons.