In this paper we study the dynamic models described by a potential V(ϕ), where ϕ represents a real scalar field, from the phenomenon of spontaneous symmetry breaking. This mechanism causes the system to have two distinct states;this can be represented in continuous media as a process of phase transition and / or the appearance of topological defects. Such defects are static solutions, stable and finite energy of a nonlinear differential equation of second order. We also present Bogomol `nyi`s equations, where we write the potential of a given model in terms of a superpotential function and the problem of solving a second-order equation reduces to finding the solutions of two first order equations whose solutions, called BPS states, identify the lowest energy states and topological sectors of the model.