Abstract
The interaction of electromagnetic radiation with a medium that is approximated by an ensemble of two-level particles is treated on a quantum-mechanical basis. The system of equations of motion obtained for the phenomena of optical and magnetic resonances has a classical analog - the system of Lagrange-Poisson equations. In the approach, propagation effects are described by the nonlinear Maxwell-Lagrange system, which can be recast as coupled systems of linear equations by the inverse scattering method. The condition of compatibility of the solutions of the linear systems yields a hierarchical set of nonlinear evolution equations: the sine-Gordon equation, the nonlinear Schroedinger equation, the Korteweg-de Vries equation.
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