Adiabatic approximation of the green function of the Helmholtz operator in almost stratified medias
Raya Pérez, Vladimir Rabinovich, Ignacio Martínez Sánchez · Russian Journal of Mathematical Physics · 2007
The Helmholtz equation describing the propagation of acoustic and electromagnetic waves in a nonhomogeneous media slowly varying in the horizontal direction is considered. The contribution of the discrete and continuous spectra of the transversal Sturm-Liouville problem to the asymptotics is studied. A uniform asymptotics for the Green function in neighborhoods of thresholds is obtained.