  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.
