Results of computer simulations concerning gain spectra of In _0.05Ga _0.95As quantum wells are presented. A novel multi-plasmon concept of a light absorption and laser gain of low-dimensional structures is comprehensively discussed. A generalized theory of multi-plasmon optical transitions in direct gap quantum wells is developed using the cumulant expansion method and fluctuation-dissipation theorem. Multi-quantum LO-phonon-plasmon optical transitions are investigated with account on coherent memory effects in quantum wells. It is shown that a red shift of the absorption edge can be caused not only by the well-known mechanism of band gap shrinkage but also by multi-plasmon transitions. The comparison with other theories and experimental data measured in In _0.05Ga _0.95As quantum wells is given.