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

Abstract

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

arXiv comment19 pages, 3 figures. Revised version published

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