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arXiv · 2510.09856

Exact BPS double-kinks in generalized $\phi^4$, $\phi^6$ and sine-Gordon models

R. Casana·E. da Hora·F. C. Simas
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Abstract

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

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R. Casana, E. da Hora, F. C. Simas. 2025-10-10. Exact BPS double-kinks in generalized $\phi^4$, $\phi^6$ and sine-Gordon models. https://doi.org/10.1140/epjc%2Fs10052-026-15362-3

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