Representation of solutions to equations of hyperbolic type

The general solutions to hyperbolic equations of the fourth and sixth orders are obtained using Vekua's method for the representation of the general solutions to elliptic equations of order $2n$ with the aid of $n$ analytic functions. It is assumed that the right-hand sides of the hyperbolic equations can be expanded in time series of sines. The systems of equations of various approximations for a prismatic thin body in terms of moments with respect to a system of Legendre polynomials can be reduced to these equations and to the hyperbolic-type equations of higher order.