2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115607Using techniques of integrable systems, we study a Weierstrass representation formula for timelike surfaces with prescribed mean curvature in Minkowski 3-space. It is shown that timelike minimal surfaces are obtained by integrating a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in Minkowski 3-space. The relationship between timelike minimal surfaces and bosonic Nambu-Goto string worldsheets in spacetime is also discussed in the appendix.16 pages, 8 figuresDifferential Geometry53A10, 53C42, 53C50, 53C80text