Bifurcations of nonlinear localized modes in disordered lattices

We analyze families of localized solutions of a nonlinear Schroumldinger equation in the presence of a disordered potential modeling a waveguide array. A coupled mode theory approximation reveals that the families of disordered lattice solitons follow a cascade of Hopf-like bifurcations. Using a perturbation method, we analyze the origins of this bifurcation structure. We find that each family of solutions is characterized by a constant number of nodes. These predictions are in agreement with the numerical results of the nonlinear Schroumldinger equation with a disordered potential.