Geometrical optics of dispersive media with turning points

The modification of the geometrical optics approximation developed in our earlier paper has been extended to problems in which the classical conditions for its validity are violated, e.g. problems in which turning points are present, and tunnelling and over-barrier reflection are studied. The application of the method to difference equations has been demonstrated by the example of the propagation of electric waves through a one-dimensional array of charged nonlinear oscillators with nearest-neighbour interactions.