The equations of motion for specific quantum systems-a two-level medium in an electromagnetic field, a ferromagnet in a magnetic field, a spin-phonon system, a superconducting tunnel junction, superconducting and superfluid media, etc.-can be reduced to nonlinear evolution equations: the sine-Gordon (SG), Korteweg-de Vries (KDV), nonlinear Schrodinger (NS), and Klein-Gordon (KG) equations. These equations represent a large class of physical processes due to the interaction of various media with strong fields of different nature. It is shown that each type of the interaction (boson-boson, boson-fermion, and fermion-fermion) is described by a certain set of evolution (SG, KDV, NS, and KG) equations. Each type of a quantum system has a classical analog