Method of difference equations in a resonator problem with a nonlinear reflector

A difference-equation approach is used to analyze a plane-parallel resonator with a nonlinear active layer. The spatial-temporal dynamics of the resonator field is analyzed in terms of the initial boundary value problem for the homogeneous wave equation with nonlinear boundary equations. The basic idea is to reduce these boundary conditions to nonlinear difference equations with a continuous argument, with subsequent application of the theory of dynamic systems.