Initial-boundary value problems for linear equations of electrodynamics with nonlinear boundary conditions

A new class of electromagnetic (EM) problems is introduced, initial-boundary value problem for linear wave equation with nonlinear boundary conditions, and methods for their solution are elaborated. Theory of nonlinear 1D maps and difference-differential equations have been applied to solve the problem. It has been shown that spatiotemporal dynamics of EM field in a resonator with nonlinear reflecting surfaces may be either regular or chaotic in spite of the major part of the system is formed by linear media. The approach may be used for analysis of chaotic processes in many electromagnetic and electronic devices.