On solving cubic-quartic nonlinear Schrödinger equation in a cnoidal trap


The recent observations of quantum droplet in ultra-cold atomic gases have opened up new avenues of fundamental research. The competition between mean-field and beyond mean-field interactions, in ultra-cold dilute alkali gases, is believed to be instrumental in stabilizing the droplets. This new understanding has motivated us to investigate the analytical solutions of a trapped cubic-quartic nonlinear Schrödinger equation (CQNLSE). The quartic contribution in the NLSE is derived from the beyond mean-field formalism of Bose–Einstein condensate (BEC). To the best of our knowledge, a comprehensive analytical description of CQNLSE is non-existent. Here, we study the existence of the analytical solutions which are of the cnoidal type for CQNLSE. The external trapping plays a significant role in the stabilization of the system. In the limiting case, the cnoidal wave solutions lead to the localized solution of bright solution and delocalized kink-antikink pair. The nonexistence of the sinusoidal mode in the current scheme is also revealed in our analysis.

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Debnath, A., Khan, A. On solving cubic-quartic nonlinear Schrödinger equation in a cnoidal trap. Eur. Phys. J. D 74, 184 (2020). https://doi.org/10.1140/epjd/e2020-10364-4

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  • Cold Matter and Quantum Gases