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.