论文标题
在求解cNoidal陷阱中的立方四分之一的非线性schrödinger方程
On Solving Cubic-Quartic Nonlinear Schrödinger Equation in a Cnoidal Trap
论文作者
论文摘要
最近对超冷原子气体中量子液滴的观察到了基本研究的新途径。据信，在超冷的碱性气体中，平均场与均值场相互作用之间的竞争被认为在稳定液滴方面具有重要作用。这些新的理解促使我们研究了捕获的立方四分之一非线性schrödinger方程（CQNLSE）的分析解决方案。 NLSE中的四分之一贡献源自Bose-Einstein冷凝物（BEC）的超出平均场形式。据我们所知，对CQNLSE的全面分析描述是不存在的。在这里，我们研究了CQNLSE的cNoidal类型的分析溶液的存在。外部陷阱在系统的稳定中起着重要作用。在限制情况下，cNoidal波解决方案导致明亮溶液的局部溶液和Decalized Kink-Antikink对。我们的分析也揭示了当前方案中正弦模式的不存在。
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, are believed to be instrumental in stabilizing the droplets. These 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.
