Riemann surface of dispersion diagram of a multilayer acoustical waveguide

A Riemann surface of a dispersion diagram of a multilayer planar waveguide is studied. Structure of this surface is linked with the transient wave phenomena in the waveguide. A method is proposed to study the dispersion diagram. The method is constituted in introducing of an artificial parameter controlling the links between the layers of the waveguide. The strength of the links varies from the full isolation to the realistic physical contact. The dependence of the solution on the artificial parameter is analytical. Using this approach it is proven that the branch points of the Riemann surface can be listed as the crossing points of the branches of non-interacting layers. A numerical procedure of finding the branch points positions is described. An explanation of the types of waves corresponding to different parts of the Riemann surface of the dispersion diagram is given.