Nonlinear phenomena caused by the quadratic interaction of electromagnetic waves in a dense charged medium (Coulomb systems, plasma) are considered: parametric generation and generation of the second harmonic of electromagnetic radiation. To determine the quadratic reaction functions describing the interaction of electromagnetic waves in the medium, an approach based on the use of explicit approximations for reaction functions with fitting parameters is applied. Parameters are found from the exact frequency moments of the reaction functions. Using data on reaction functions, the conditions for the experimental implementation of these phenomena in a laboratory dense plasma in a constant magnetic field were evaluated.