  The quantum optical problem of the propagation of electromagnetic waves in a
nonlinear waveguide is related to the solutions of the classical nonstationary
harmonic oscillator using the method of linear integrals of motion [ Malkin
et.al., Phys Rev. 2D (1970) p.1371 ]. An explicit solution of the classical
oscillator with a varying frequency, corresponding to the light propagation in
an anisotropic waveguide is obtained using the expressions for the quantum
field fluctuations. Substitutions have been found which allow to establish
connections of the linear and quadratic invariants of Malkin et.al. to several
types of invariants of quadratic systems, considered in later papers. These
substitutions give the opportunity to relate the corresponding quantum problem
to that of the classical two-dimensional nonstationary oscillator, which is
physically more informative.

Quantum Physics