https://doi.org/10.1140/epjc/s10052-025-14211-z
Regular Article - Theoretical Physics
Sine-Gordon kink lattice
1
Coordenação do Curso de Bacharelado Interdisciplinar em Ciência e Tecnologia, Universidade Federal do Maranhão, 65080-805, São Luís, Maranhão, Brazil
2
Centro de Física e Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, 4169-007, Porto, Portugal
3
Departamento de Física, Universidade Federal do Maranhão, Campus Universitário do Bacanga, 65085-580, São Luís, Maranhão, Brazil
Received:
12
November
2024
Accepted:
21
April
2025
Published online:
3
May
2025
We consider an extended model with two real scalar fields, 
and 
. The first sector is controlled by the sine-Gordon superpotential, while the second field is submitted to the 
one. The fields mutually interact via a nontrivial coupling function 
that also changes the kinematics of 
. We briefly review the implementation of the Bogomol’nyi–Prasad–Sommerfield (BPS) prescription (Prasad and Sommerfield in Phy Rev Lett 35:12 1975, Bogomolny in Sov J Nucl Phys 24:449, 1976). 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.
© The Author(s) 2025
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