2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33427The initial-value problem for cylindrical gravitational waves is studied through the development of the inverse scattering method scheme. The inverse scattering transform in this case can be viewed as a transformation of the Cauchy data to the data on the symmetry axis. Riemann-Hilbert problem, which serves as inverse transformation, is formulated in two different ways. We consider Einstein-Rosen waves to illustrate the method.11 pages, LaTeX, no figures, discussion added, some misprints correctedGeneral Relativity and Quantum Cosmologytext