On applied aspects of studing roots of dispersions equations on the other sheets of the complex plane

Under a quontitative estimation of interference wave fields by using the methods of the theory of functions, the initial path of integration is deformed on some complex plane $(\zeta)$. As a result of such a deformation the countor $(\lambda)$ may be places on other sheets of the Riemann surface of the plane $(\zeta)$. It forces us to study integrands, in particular, a dispersion equation of the problem on the other sheets of the plane $(\zeta)$. Similar equations are discussed in the case of the problem for a layer being in contact with two elastic half-spaces. Bibl. 3 titles, ill. 9.