Wave-equation integrals in a spacetime with the metric of a gravitational plane wave

General analytical solutions to the scalar wave equation and the (spinor) Maxwell equations on the metric background of a weak gravitational plane wave are obtained on the basis of a previously determined integral equation that is equivalent to the wave equation with variable coefficients. These solutions are presented in the form of a generalized retarded potential or a generalized Kirchhoff formula plus a surface integral. An equation for the light cone corresponding to the moving surface of the wave front is derived along with an expression for the relevant Sobolev function. Different forms of the light-cone equation and the invariance of the Sobolev function are examined.