Title: Transient phenomena in a three-layer waveguide and the analytical structure of the dispersion diagram,
Abstract: Excitation of waves in a three-layer acoustic wavegide is studied. The wave
field is presented as a sum of integrals. The summation is held over all
waveguide modes. The integration is performed over the temporal frequency axis.
The dispersion diagram of the waveguide is analytically continued, and the
integral is transformed by deformation of the integration contour into the
domain of complex frequencies. As the result, the expression for the fast
components of the signal (i.e. for the transient fields) is simplified.
The structure of the Riemann surface of the dispersion diagram of the
waveguide is studied. For this, a family of auxiliary problems indexed by the
parameters describing the links between layers is introduced. The family
depends on the linking parameters analytically, and the limiting case of weak
links can be solved analytically.