2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/201996We systematically classify all possible Bogomol'nyi-Prasad-Sommerfield (BPS) equations in Euclidean dimension $d\leq8$. We discuss symmetries of BPS equations and their connection with the self-dual Yang-Mills equations. Also, we present a general method allowing to obtain the BPS equations in any dimension. In addition, we find all BPS equations in the Minkowski space of dimension $d\leq6$ and apply the obtained results to the supersymmetric Yang-Mills theories. In conclusion, we discuss the possibility of using the classification to construct soliton solutions of the low-energy effective theory of the heterotic string.31 pages, LaTeXHigh Energy Physics - Theorytext