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arXiv · 2510.07012

Localized structures in two-field systems: exact solutions in the presence of Lorentz symmetry breaking and explicit connection with geometric constraints

G. H. Bandeira·D. Bazeia·G. S. Santiago·Ya. Shnir
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Abstract

We investigate a class of models described by two real scalar fields in two-dimensional spacetime. The study focuses mainly on the presence of exact static solutions which satisfy the first-order formalism, in models constructed to engender Lorentz symmetry violation. We start by exploring a direct connection between Lorentz breaking and geometric constraint, as experimentally examined in the case of domain walls in geometrically constrained magnetic materials. By means of a specific choice of functions, we show that imposing geometric constraint within the Lorentz-violating framework recovers the exact solutions of the corresponding Lorentz-invariant theory. Furthermore, we extend the investigation to new models that go beyond reproducing the Lorentz invariant geometrically constrained solutions, revealing that it remains possible to parametrize the first-order equation of one of the fields through a suitably redefined coordinate.

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G. H. Bandeira, D. Bazeia, G. S. Santiago, Ya. Shnir. 2025-10-08. Localized structures in two-field systems: exact solutions in the presence of Lorentz symmetry breaking and explicit connection with geometric constraints. https://doi.org/10.1088/1402-4896/ae4f34

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