2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/196254We construct a family of supersymmetric solutions in time-dependent backgrounds in supergravity theories. One class of the solutions are intersecting brane solutions and another class are brane solutions in pp-wave backgrounds, and their intersection rules are also given. The relation to existing literature is also discussed. An example of D1-D5 with linear null dilaton together with its possible dual theory is briefly discussed.12 pages, corrected typo, added reference, to appear in Phys. Rev. DHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext