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Excitation of waves in a three-layer acoustic wavegide is studied. The wavefield is presented as a sum of integrals. The summation is held over allwaveguide modes. The integration is performed over the temporal frequency axis.The dispersion diagram of the waveguide is analytically continued, and theintegral is transformed by deformation of the integration contour into thedomain of complex frequencies. As the result, the expression for the fastcomponents of the signal (i.e. for the transient fields) is simplified.  The structure of the Riemann surface of the dispersion diagram of thewaveguide is studied. For this, a family of auxiliary problems indexed by theparameters describing the links between layers is introduced. The familydepends on the linking parameters analytically, and the limiting case of weaklinks can be solved analytically.

Transient phenomena in a three-layer waveguide and the analytical structure of the dispersion diagram