On the connection between Loev's modes and the set of supercritical reflective waves

On the example of Loev's problem the relations connecting two exact representations for solution are considered: the representation which containing in explicit form the damping (leaking) and nondamping modes (the residues in the dispersion equations' roots) and the representation based on factorization of interference wave field in the serie of geometric progression. In the last case for each such term it is possible to associate some general ray for the wave of definite multiplicity propagation inside the layer. By contour integral methods the correspondence between the set of multiple waves and interference mode is determined. Bibliography: 1 title.