Solitonlike structures and their self-similarity in nonlinear Fibonacci multilayered media

Switching from low to total transmission in a nonlinear Fibonacci multilayered medium is examined. It is found that this switching is due to the formation of solitonlike structures characterized by a ${\mathrm{sech}}^2$ intensity distribution, which results from a delicate interplay between dispersion and nonlinearity in the medium. These are shown to possess the remarkable properties of scaling and self-similarity.