Deformation of sine-Gordon two-soliton solutions in $φ^4$ kink-antikink configurations

In this work, we construct analytical kink-antikink $(K\bar{K})$ configurations in the non-integrable $φ^4$ model by mapping exact solutions of the integrable sine-Gordon system via a field deformation. This procedure yields two distinct classes of configurations, parametrized by the initial half-se