Applied aspects of studying roots of dispersion equations on nonprincipal sheets of a complex plane (Q1388947)

In order to study the qualitative behaviour of the interference wave field in layered media, one represents the solution (the displacement) as an integral containing a kernel \(V\), which is also representable as an integral performed in a complex plane \(\lambda\). The path along which the integration must be performed depends on the location of the roots of the dispersion equation. Therefore, one must operate with some cuts in \(\lambda\) plane, in this way constituing the initial sheet. Sometimes, in order to express the kernel \(V\) in a more adequate form, one modifies the initial path of integration, so that it is possible to achieve other sheets. This paper investigates the effects of changing the initial sheet on the expression for the solution. A particular attention is paid to the form of the dispersion equation which describes the wave phenomena in layered media.