  In this paper we deal with a nonlinear Schr\"{o}dinger equation with chaotic,
random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton
evolution, with the strength of the nonlinearity perturbed in the space and
time coordinates and to check its robustness under these conditions. Comparing
with a real system, the perturbation can be related to, e.g., impurities in
crystalline structures, or coupling to a thermal reservoir which, on the
average, enhances the nonlinearity. We also discuss the relevance of such
random perturbations to the dynamics of Bose-Einstein Condensates and their
collective excitations and transport.
