In this work, the propagation of an ultrasonic nonlinear wave through a multiple scattering medium is experimentally studied. The interaction between multiple scattering and nonlinear phenomena is analyzed by the cross correlation of the scattered field. This approach corresponds to a virtual time reversal. The cross correlated field is focused in both time and space. In linear regime, it is known that the focal width decreases as the thickness of the multiple scattering medium is increased. In this work, it is shown that this behavior is followed by a nonlinear wave and its harmonics. Moreover, due to the spectral richness of the nonlinear wave, the focal width is reduced in the nonlinear regime. This fact allows for the conclusion that the harmonics propagate following a linear scattering equation, although a nonlinear regime is required to generate them. Beside the experimental work, an estimation on the order of magnitude of the parameters that quantify nonlinearity and scattering phenomena is performed. The estimation shows that the Lighthill-Westervelt equation is as an accurate theoretical model for describing the multiple scattering of a nonlinear wave in the experiments.