On Bogomol'nyi Equations of Classical Solutions

We review the Bogomol'nyi equations and investigate an alternative route in obtaining it. It can be shown that the known BPS equations can be derived directly from the corresponding Euler-Lagrange equations via separation of variables, without having to appeal to the Hamiltonian. We apply this technique to the Dirac-Born-Infeld solitons and obtained the corresponding equations and the potentials. This method is suitable for obtaining the first-order equations and determining the allowed potentials for noncanonical defects.