Exploring the vicinity of the Bogomol'nyi-Prasad-Sommerfield bound

We investigate systems of real scalar fields in bidimensional spacetime, de aling with potentials that are small modifications of potentials that admit supersymmetric extensions. The modifications are controlled by a real para meter, which. allows the implementation of a perturbation procedure when su ch a parameter is small. The procedure allows one to obtain the energy and topological charge in closed forms, up to first order in the parameter. We illustrate the procedure with some examples. In particular, we show how to remove the degeneracy in energy for the one-field and the two-field solutio ns that appear in a model of two real scalar fields.