Soliton interactions and the formation of solitonic patterns.

摘要

From the stripes of a zebra, to the spirals of cream in a hot cup of coffee, we are surrounded by patterns in the natural world. But why are there patterns? Why drives their formation? In this thesis we study some of the diverse ways patterns can arise due to the interactions between solitary waves in nonlinear systems, sometimes starting from nothing more than random noise.; What follows is a set of three studies. In the first, we show how a nonlinear system that supports solitons can be driven to generate exact (regular) Cantor set fractals. As an example, we use numerical simulations to demonstrate the formation of Cantor set fractals by temporal optical solitons. This fractal formation occurs in a cascade of nonlinear optical fibers through the dynamical evolution of a single input soliton.; In the second study, we investigate pattern formation initiated by modulation instability in nonlinear partially coherent wave fronts and show that anisotropic noise and/or anisotropic correlation statistics can lead to ordered patterns such as grids and stripes.; For the final study, we demonstrate the spontaneous clustering of solitons in partially coherent wavefronts during the final stages of pattern formation initiated by modulation instability and noise. Experimental observations are in agreement with theoretical predictions and are confirmed using numerical simulations.