https://doi.org/10.1140/epjp/s13360-025-06525-4
Regular Article
Dynamics of positons and hybrid solutions for a generalized Gross–Pitaevskii equation in Bose–Einstein condensates
1
College of Mathematics Science, Inner Mongolia Normal University, 010022, Hohhot, People’s Republic of China
2
Center for Applied Mathematical Science, Inner Mongolia, 010022, Hohhot, People’s Republic of China
3
Key Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application, Ministry of Education (IMNU), 010022, Hohhot, People’s Republic of China
Received:
18
March
2025
Accepted:
5
June
2025
Published online:
29
June
2025
Using the degenerate Darboux transformation (DDT), we obtain N-positon solutions of the generalized Gross–Pitaevskii equation by taking the limit 
from the N-soliton solution and applying higher-order Taylor expansion. Using the method of the modulus square decomposition, n-positon is decomposed into n single soliton solutions. Our study reveals that nonlinear effects compress the positon solutions and alter their directions. We also derive Nth-order breather–positon (B–P) solutions with DDT, finding that nonlinear terms compress these B–Ps but do not affect their periods. Additionally, we discuss hybrid solutions and provide corresponding three-dimensional map.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
