2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/186929Exact solutions of Einstein's vacuum equations are considered which describe gravitational waves with distinct wavefronts. A family of such solutions presented recently in which the wavefronts have various geometries and which propagate into a number of physically significant backgrounds is here related to an integral representation which is a generalisation of the Rosen pulse solution for cylindrical waves. A nondiagonal solution is also constructed which is a generalisation of the Rosen pulse, being a cylindrical pulse wave with two states of polarization propagating into a Minkowski background. The solution is given in a complete and explicit form. A further generalisation to include electromagnetic waves with a distinct wavefront of the same type is also discussed.14 pages, Plain TeX, no figures. To appear in Classical and Quantum GravityGeneral Relativity and Quantum Cosmologytext