Dispersive Behaviours in Complex Structures

In the framework of the Scale Relativity Theory, a fractal Korteweg-de Vries-type equation for describing dispersive behaviours of any complex structure is obtained. In the one-dimensional case, the general solution of this equation show that the dispersive behaviours of any complex structure are given by means of cnoidal oscillation modes. Through these modes degeneration, dispersive behaviours of soliton, soliton-package, harmonic etc. result.