https://doi.org/10.1140/epjc/s10052-026-15575-6
Regular Article - Theoretical Physics
Spontaneous symmetry breaking for solitons and local meta-stability: an elliptic functions based formulation
1
Instituto de Física, Universidad Autónoma de Puebla, Apartado postal J-48, 72570, Puebla, Pue., Mexico
2
Escuela de Ciencias, Universidad Autónoma Benito Juárez de Oaxaca, Apartado postal 68120, Oaxaca de Juárez, Oaxaca, Mexico
a
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Received:
15
September
2025
Accepted:
18
March
2026
Published online:
5
April
2026
Abstract
We show that in an elliptic function based formulation for fields with large amplitudes, the rolling down of solitons towards the degenerate vacua can be described as transitions through local meta-stable potentials; the kink-like solitons constructed locally around the maxima of the potential will roll down into the vacua without changing their profiles and their energies, but amplifying their amplitudes and their topological charges. Furthermore, the cusp-like solitons trapped at vacua will admit a nonlinear decomposition in terms of fundamental solitons with different profiles, energies, amplitudes, and topological charges; a scale-probe is proposed in order to reveal the different scales for those vacuum fundamental solitons. The possibility for a vacuum-vacuum tunneling for solitons is addressed.
© The Author(s) 2026
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