2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/189744We give the relation between the solutions generated by the inverse scattering method and the Bäcklund transformation applied to the vacuum five-dimensional Einstein equations. In particular, we show that the two-solitonic solutions generated from an arbitrary diagonal seed by the Bäcklund transformation are contained within those generated from the same seed by the inverse scattering method.17 pages, Some references are added, to be published in Phys.Rev.DHigh Energy Physics - Theorytext