Effects of chaotic perturbations on a nonlinear system undergoing two-soliton collisions

In this work, we present a numerical study of two-soliton collisions in a system described by a cubic (Kerr-type) nonlinear Schrödinger equation whose nonlinearity has small chaotic imperfections. We use a logistic map in order to obtain a chaotic perturbation, where by defining the values of its seed and the interaction parameter, one can observe a disorder in the nonlinearity of the system. This disorder was varied by changing the parameter values and controlled via the Lyapunov exponent, however, always maintaining a fixed amplitude. We verified a direct relationship between the value of the Lyapunov coefficient and the formation of two-soliton bonded/unbonded states.