Exact BPS double-kinks in generalized φ ⁴, φ ⁶ and sine-Gordon models

We consider a $$(1+1)$$ ( 1 + 1 ) -dimensional theory with a single real scalar field φ ϕ whose kinematics is modified by a generalizing function f(φ ) f ( ϕ ) . After briefly reviewing its Bogomol’nyi–Prasad–Sommerfield (BPS) structure, we focus on a particular f(φ ) f ( ϕ ) to obtain analytic BPS double-kink solutions in three different models governed by the φ ⁴ ϕ 4 , φ 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 φ ⁴ ϕ 4 and sine-Gordon superpotentials. Whereas, for the φ ⁶ ϕ 6 superpotential, the BPS energy profiles form asymmetric two-lumps.