2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/52305We obtain background independent solutions for an open string ending on D-brane, in variable external fields. Explicit solution of the boundary conditions is given for background metric and NS-NS two-form gauge field, depending on the coordinates of the transverse to the Dp-brane directions. Extension of the constraint algebra is proposed and discussed from both Hamiltonian and Lagrangian approach viewpoint.LaTeX, 14 pages, no figures; V2: cosmetic changes, invited paper for the Volume "Frontiers in Field Thory", O. Kovras, ed. (Nova Science Publishers, NY)High Energy Physics - Theorytext