Abstract We consider a (1+1) (1 + 1) -dimensional theory with a single real scalar field ϕ whose kinematics is modified by a generalizing function f () f (ϕ). After briefly reviewing its Bogomol’nyi–Prasad–Sommerfield (BPS) structure, we focus on a particular f () f (ϕ) to obtain analytic BPS double-kink solutions in three different models governed by the ⁴ ϕ 4, ⁶ ϕ 6, and sine-Gordon superpotentials. In all cases, the resulting double-kinks approach the vacuum values by following an exponential decay, with the generalizing function controlling its dependence on x and mass. We also calculate the BPS bound explicitly and study how the double kinks behave near the origin. The energy distribution of the novel BPS states engenders symmetric two-lump profiles for the ⁴ ϕ 4 and sine-Gordon superpotentials. Whereas, for the ⁶ ϕ 6 superpotential, the BPS energy profiles form asymmetric two-lumps.
Casana et al. (Sun,) studied this question.