Criterion of existence of longitudinally inhomogeneous traveling waves in nonlinear electrodynamics

The criterion referred to in the title is established solely on the basis of the behavior of the function ( u ) u 4 , where u is the amplitude of the field in question and ( u ) is the nonlinear permittivity of the medium involved. The criterion is used to discuss the possibility of realization of one-dimensional longitudinally inhomogeneous waves under various conditions and, in particular, in nonlinear optics.