Self-similarity and fractals driven by soliton dynamics

Summary form only given. Solitons are a fairly general nonlinear phenomena, appearing in very many nonlinear wave systems in nature. Very often, the solitons of a given system are all self-similar to each other. In other words, there is a simple scaling relation for their size and intensity that maps all the solitons onto each other. This happens when the underlying equation describing the system does not have any natural length scale appearing in it, a good example is the cubic nonlinear Schrodinger equation (NLSE).