https://doi.org/10.1140/epjp/s13360-026-07379-0
Regular Article
Matter wave dynamics and interactions of (2+1)-dimensional Bose–Einstein condensate with gain/loss atoms in magnetic and time-dependent laser fields
1
Pure physics Laboratory: Group of nonlinear physics and complex systems, Department of Physics, Faculty of Science, University of Douala, P.O. Box 24157, Douala, Cameroon
2
Centre for Atomic Molecular Physics and Quantum Optics (CEPAMOQ), Faculty of Science, University of Douala, P.O. Box 8580, Douala, Cameroon
3
Department of Physics, University of Bamenda, P.O. Box 39, Bamenda, Cameroon
4
Instituto de Fisica Téorica, UNESP – Universidade Estadual Paulista, 01140-070, Sao Paulo, Brazil
5
Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana
a
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Received:
18
November
2025
Accepted:
29
January
2026
Published online:
11
February
2026
Abstract
In this work, we investigate the modified Gross-Pitaevskii equation in two dimensions describing high-dimensional Bose–Einstein condensates under atomic gain/loss, a harmonic trapping potential, and external magnetic and time-dependent laser fields. By applying Hirota’s bilinear method, we derive exact analytical one- and two-soliton solutions, from which we construct localized excitations such as second-order rogue matter waves and line-solitons. A detailed analysis reveals that the amplitude and stability of these nonlinear structures can be effectively controlled through the parameters of higher-order interactions, as well as by the atomic gain/loss term and the coefficient of the harmonic potential. In contrast to line-soliton, the second-order rogue matter waves exhibit curved trajectories whose shape and direction are strongly influenced by the linear magnetic field parameter, acting as an external force capable of guiding and stabilizing the propagation of localized structures. The time-dependent laser field, characterized by its amplitude and frequency, introduces temporal modulation and periodic oscillations in the density profile, allowing direct control over the frequency and amplitude of the matter-wave dynamics. The interplay between the magnetic and laser fields reveals a new mechanism for manipulating nonlinear excitations, where the magnetic field governs the spatial direction while the laser field modulates temporal coherence. Furthermore, the time-dependent gain/loss term and the higher-order interaction parameter generate collapse and resurgence regions during the evolution of rogue matter waves, revealing the quasi-integrable nature and local energy exchange of the system. The combined influence of the magnetic and laser fields thus provides an efficient and flexible means of steering, trapping, and stabilizing nonlinear excitations in Bose-Einstein condensates. These findings open new perspectives for the coherent experimental control of matter waves and for the development of quantum technologies based on the tunable dynamics of nonlinear matter-wave phenomena.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
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.
