Symmetry break in a scalar field theory in a $(1 + 1)$-spacetime

We consider in this work a relativistic scalar field theory in a $(1+1)$-Minkowski spacetime for a class of periodic potentials. These potentials exhibit solutions known as kinks and antikinks with topological charges, energy density, and mass dependent on the potential's parameters. We break the symmetry from a vacuum expectation value ($vev$) zero for a non-zero $vev$, which means that the supersymmetry (SUSY) has spontaneously broken.