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We investigate systems of real scalar fields in bidimensional spacetime,dealing with potentials that are small modifications of potentials that admitsupersymmetric extensions. The modifications are controlled by a realparameter, which allows implementing a perturbation procedure when suchparameter is small. The approach allows obtaining the energy and topologicalcharge in closed forms, up to first order in the parameter. We illustrate theprocedure with some examples. In particular, we show how to remove thedegeneracy in energy for the one-field and the two-field solutions that appearin a model of two real scalar fields.Comment: Revtex, 9 pages, To be published in J. Phys.

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