article · Annals of Physics
Bose–Einstein condensates are formed when a bosonic gas is cooled to a temperature near absolute zero. When this occurs, quantum properties that are microscopic become macroscopic, facilitating their study. We have studied matter waves in the Gross–Pitaevskii equation subject to a trap Kapitza potential, which is a quantum analog of the classical inverse Kapitza pendulum. Since this specific system was recently experimentally realized with ultracold atoms for the first time, exploring the theoretical models of this system is, therefore, significant and up-to-date. To find the analytical solutions of the corresponding Gross–Pitaevskii equation with such potential, the extended hyperbolic tangent function method was chosen, which leads to soliton solutions. The new class of solutions found in this work, written in terms of Mathieu functions, was used to analyze the influence of the Kapitza potential free model parameters on the soliton dynamics within the condensate. These mainly include dark and dark-bright solitons. Our findings suggest that there are specific classes of parameters of the system for which bright solitons do not exist.
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DOI: 10.1016/j.aop.2026.170513
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