Constructing BPS Vortex Solutions in the Kruglov-Higgs System via the BPS Lagrangian Method
Ury Ubaydillah (a*), Handhika S. Ramadhan (a)

a) Departemen Fisika, FMIPA, Universitas Indonesia, Depok 16424, Indonesia
*uryubaydillah11[at]gmail.com

Abstract

Nonlinear electrodynamics has long offered a productive route toward understanding electromagnetic fields in high-energy regimes, yet most studies of BPS vortex solutions remain concentrated on the Maxwell-Higgs and Born-Infeld-Higgs models. This work addresses that gap by constructing BPS vortex solutions in the Kruglov-Higgs system - a model coupling Kruglov nonlinear electrodynamics to an Abelian (U(1)) Higgs field - using the BPS Lagrangian method. To the best of our knowledge, this is the first application of the BPS Lagrangian method to the Kruglov model, representing a new entry in the broader map of BPS vortex solutions across nonlinear electrodynamic theories.
The Kruglov model is characterized by a dimensionless parameter (\sigma) that allows access to a wider class of nonlinearities than Born-Infeld alone. The analysis is performed for three values of (\sigma): (\sigma = 1) as the Maxwell limit, (\sigma = 1/2) as the Born-Infeld limit, and (\sigma = 1/4) as a representative of the regime where Kruglov nonlinearity is strongest and most distinct from both reference models. Together, these three cases enable a systematic mapping of how (\sigma) reshapes the BPS equations and the resulting scalar potential structure.
Across all cases, the BPS string tension is found to be universal, (\mu = 2\pi|n|), and field profiles are obtained numerically via a shooting method, with results validated against the Maxwell limit as (\beta \to 0).

Keywords: BPS vortex, Kruglov nonlinear electrodynamics, Abelian Higgs mechanism, BPS Lagrangian method.

Topic: Theory, Nuclear, and Particle Physics