Maxwell-lagrange system in the theory of optical and magnetic resonances

Quantum-mechanical approach is used to tackle the problem of interaction of electromagnetic field with medium which is approximated by an ensemble of two-level particles. A quantum-mechanical system of equations of motion is obtained for phenomena of optical and magnetic resonance. This system has a classical analogue, the system of Lagrange–Poisson equations. Propagation effects in the approach under consideration are described by the nonlinear Maxwell–Lagrange system which can be presented in the form of connected systems of linear equations of inverse scattering theory. A hierarchy of nonlinear evolutionary equations is derived which includes sine-Gordon, nonlinear Schrödinger and Korteveg–de Vries equations.