Exact BPS double-kinks in generalized $ϕ^4$, $ϕ^6$ and sine-Gordon models
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| Format: | Preprint |
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2025
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| _version_ | 1866914317312458752 |
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| author | Casana, R. da Hora, E. Simas, F. C. |
| author_facet | Casana, R. da Hora, E. Simas, F. C. |
| contents | We consider a $(1+1)$-dimensional theory with a single real scalar field $ϕ$ whose kinematics is modified by a generalizing function $f(ϕ)$. After briefly reviewing its Bogomol'nyi-Prasad-Sommerfield (BPS) structure, we focus on a particular $f(ϕ)$ to obtain analytic BPS double-kink solutions in three different models governed by the $ϕ^4$, $ϕ^6$, 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 $ϕ^4$ and sine-Gordon superpotentials. Whereas, for the $ϕ^6$ superpotential, the BPS energy profiles form asymmetric two-lumps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09856 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact BPS double-kinks in generalized $ϕ^4$, $ϕ^6$ and sine-Gordon models Casana, R. da Hora, E. Simas, F. C. High Energy Physics - Theory Pattern Formation and Solitons Exactly Solvable and Integrable Systems We consider a $(1+1)$-dimensional theory with a single real scalar field $ϕ$ whose kinematics is modified by a generalizing function $f(ϕ)$. After briefly reviewing its Bogomol'nyi-Prasad-Sommerfield (BPS) structure, we focus on a particular $f(ϕ)$ to obtain analytic BPS double-kink solutions in three different models governed by the $ϕ^4$, $ϕ^6$, 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 $ϕ^4$ and sine-Gordon superpotentials. Whereas, for the $ϕ^6$ superpotential, the BPS energy profiles form asymmetric two-lumps. |
| title | Exact BPS double-kinks in generalized $ϕ^4$, $ϕ^6$ and sine-Gordon models |
| topic | High Energy Physics - Theory Pattern Formation and Solitons Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2510.09856 |