https://doi.org/10.1140/epjc/s10052-025-14470-w
Regular Article - Theoretical Physics
A Bogomol’nyi–Prasad–Sommerfield bound with a first-order system in the 2D Gross–Pitaevskii equation
1
Centro de Estudios Científicos (CECs), Casilla, 1469, Valdivia, Chile
2
Universidad San Sebastáin, sede Valdivia, General Lagos 1163, 5110693, Valdivia, Chile
3
Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Casilla 567, 5090000, Valdivia, Chile
4
IPNP-Faculty of Mathematics and Physics, Charles University, V Holešovickách 2, 18000, Prague 8, Czech Republic
Received:
9
March
2025
Accepted:
24
June
2025
Published online:
19
August
2025
A novel Bogomol’nyi–Prasad–Sommerfield (BPS) bound for the Gross–Pitaevskii equations in two spatial dimensions is presented herein. The energy can be bounded from below in terms of the combination of two boundary terms, one related to the vorticity (but “dressed” by the condensate profile) and the second to the “skewness” of the configurations. The bound is saturated by configurations that satisfy a system of two first-order partial differential equations. When such a BPS system is satisfied, the Gross–Pitaevskii equations are also satisfied. The analytic solutions of this BPS system in the present manuscript represent configurations with fractional vorticity living in an annulus. Using these techniques, we present the first analytic examples of this kind. The hydrodynamic interpretation of the BPS system is discussed, and the implications of these results are outlined.
© The Author(s) 2025
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