I have read about solitons and they seem to be a big deal as a phenomenon. The definition I find from wikipedia is that solitons are characterized by the following three properties:
They are of permanent form
They are localized within a region
They can interact with other solitons, and emerge from the collision unchanged, except for a phase shift.
Well, the d'Alembert solution to the wave equation $F(x-ct)$ and $G(x+ct)$ has these properties. We can always choose $F$ and $G$ to be functions with compact support, hence satisfying 2. They are of permanant form as well. I'm not quite sure how to quantify 'interact' in property 3.
So why arent these solutions considered to be 'solitons'?