Existence problems in steady state theory for electromagnetic waves in weakly nonlinear media

A theory of steady state nonlinear wave propagation is discussed. Here "steady state" implies that wave parameters remain invariant in time and space domains. Conditions for the existence of such a state are analyzed. A detailed discussion is given for a quadratic homogeneous medium. The necessary conditions providing a steady state, and concerning medium properties and wave amplitudes, are derived in closed form for a quadratic dispersive medium. It is shown that a steady state may be achieved for small amplitude waves where a certain relation between the input amplitude and the medium dispersive and nonlinear properties is satisfied. The case of very weak dispersion is discussed separately.