Analytical solutions of a CQNLSE with a source

Abstract

Motivated by the recent observation of quantum droplet and its beyond mean-field description, we investigate the existence of cnoidal waves in a driven cubic-quartic nonlinear Schr¨odinger equation (CQNLSE), as the most simplistic modeling of beyond mean-field formalism of Bose-Einstein condensate (BEC) can be traced in the framework of CQNLSE. To the best of our knowledge, a comprehensive analytical description of CQNLSE is nonexistent. We check for the existence of the analytical solutions of forced CQNLSE. The stabilization of the system necessitates the inclusion of the source term. We derive analytical cnoidal wave solutions which are both localized as well as nonlocalized type. Further we reveal the existence of bright soliton like structure, a flat valley like structure and w-type solitons. We are also able to see the non existence of sinusoidal modes.