Ing. Antonín Krpenský

There is only a limited amount of known analytical solutions to the Pridmore-Brown equation, mostly employing asymptotic behavior for a certain frequency limit and specifically chosen flow profiles. In this paper, we show the possibility of transformation of the Pridmore-Brown equation into the Schrödinger-like equation for the case of two-dimensional homentropic mean flow without critical layers. The corresponding potential that depends on the mean flow profile can then be approximated by a quartic polynomial, leading to a triconfluent Heun equation whose solution based on the triconfluent Heun functions is generally known. The quality of this approximation procedure is presented for the case of symmetric polynomial flow profiles for various values of polynomial order and the Mach number. A more detailed example is then shown for a quadratic mean flow profile, where the solution is accurate up to the third order of the Mach number.

This paper deals with the solution of the model equations, which describes the propagation of the surface Love-type waves in a waveguide structure consisting of a lossy isotropic inhomogeneous layer placed on a viscoelastic homogeneous substrate. The paper points to the possibility of using the triconfluent Heun differential equation to solve the model equation. The exact analytical solution within the inhomogeneous layer is expressed by the triconfluent Heun functions. The exact solutions are general in the sense that only the internal parameters of the triconfluent Heun functions can change the spatial dependencies of the material parameters in the inhomogeneous layer's thickness direction. Based on the comparison, the limits of the WKB method applicability are discussed. It is further demonstrated that substrate losses affect the dispersion characteristics only to a small extent. Using examples in which the surface layer is represented by functionally graded materials, it was shown that the distance between the modes can be influenced through those materials.