The Cauchy problem for linear inhomogeneous wave equations with variable coefficients

In this paper, we present a new analytical formula for the Cauchy problem of the linear inhomogeneous wave equation with variable coefficients. The formula gives a much simpler solution than that given by the classical Poisson formula. The derivation is based on Duhamel's Principle and the theory of pseudodifferential operator. An example is solved by using the formula to illustrate the feasibility.