2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123403Certain explicit solutions to the Korteweg-de Vries equation in the first quadrant of the $xt$-plane are presented. Such solutions involve algebraic combinations of truly elementary functions, and their initial values correspond to rational reflection coefficients in the associated Schrödinger equation. In the reflectionless case such solutions reduce to pure $N$-soliton solutions. An illustrative example is provided.17 pages, no figuresMathematical PhysicsExactly Solvable and Integrable Systems37K15; 35Q51; 35Q53text