The dynamics of isotopically selective interactions between the radiation of three pulsed lasers and atoms with a four-levels scheme has been studied. Starting from the time-dependent Schr?dinger equation with the rotating-wave approximation, we applied Sylvester theorem to the dynamic equations associated with near-and off-resonant excitations, respectively. We obtained the explicit expressions for the four-levels occupation probabilities. The analytic treatment explored the properties of coherent oscillations occurred in the atomic excitatioi. processes with intense mono-chromatic lasers. The conditions under which the population inversion takes place are derived from near-resonant excitations. The criteria to select the basis parameters of pulsed lasers involved in the process are also provided.