Wave phenomena in inhomogeneous media

An expression is derived for the difference between two fundamental solutions of the partial differential equations with variable coefficients which govern the same physical phenomenon (such as the propagation of acoustic waves in oceans or the vibrations of complex structures) in two different physical media. The expression for the difference is derived in the form of a converging series. Using a Ritz-Galerkin method, a linear algebraic system is obtained, the solution of which yields an approximate representation of the difference between the fundamental solutions. The convergent series is derived from the analytical solution of the linear algebraic system.