Several experimental groups reported the evidence of multiple periodic modulations of nuclear decay constants which amplitudes are of the order 0.05% and have periods of one year, 24 hours or about one month. We argue that these deviations from radioactive decay law can be explained as the effect of small nonlinear corrections to standard quantum mechanics, in particular, to Hamiltonian of quantum system interaction with gravitational field. It's shown that modified Doebner-Goldin nonlinear model predicts the similar decay parameter variations under influence of Sun gravity.