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High Energy Physics - Theory

arXiv:2411.00512 (hep-th)
[Submitted on 1 Nov 2024]

Title:Sine-Gordon kink lattice

Authors:E. da Hora, C. dos Santos, Fabiano C. Simas
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Abstract:We consider an extended model with two real scalar fields, $\phi(x,t)$ and $\chi(x,t)$. The first sector is controlled by the sine-Gordon superpotential, while the second field is submitted to the $\chi^4$ one. The fields mutually interact via a nontrivial coupling function $f(\chi)$ that also changes the kinematics of $\phi$. We briefly review the implementation of the Bogomol'nyi-Prasad-Sommerfield (BPS) prescription. We then solve the resulting BPS equations for two different interactions $f$. The first one leads to a single kink-kink configuration, while the second one gives rise to a inhomogeneous sine-Gordon kink lattice. We study the linear stability of these new solutions, focusing on their translational modes. We also explore how the strength of the mutual interaction affects the BPS profiles. In particular, we show that a homogeneous lattice with identical kinks is attained in the regime of extremely strong interactions.
Comments: 18 pages, 3 figures. Suggestions are welcome
Subjects: High Energy Physics - Theory (hep-th); Pattern Formation and Solitons (nlin.PS); Exactly Solvable and Integrable Systems (nlin.SI)
Cite as: arXiv:2411.00512 [hep-th]
  (or arXiv:2411.00512v1 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.2411.00512

Submission history

From: Eduardo da Hora [view email]
[v1] Fri, 1 Nov 2024 11:03:51 UTC (205 KB)
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