Regular Article

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

Department of Physics, School of Engineering and Applied Sciences, Bennett University, Greater Noida, Uttar Pradesh 201310, India

^a e-mail: ayan.khan@bennett.edu.in

Received: 1 July 2020
Received in final form: 12 August 2020
Accepted: 17 August 2020
Published online: 15 September 2020

Abstract

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.