标题： 一维立方-五次Gross-Pitaevskii方程在势阱势中的玻色-爱因斯坦凝聚体中 显示英文标题

标题： One-dimension cubic-quintic Gross-Pitaevskii equation in Bose-Einstein condensates in a trap potential

摘要： 通过新的通用变分方法，我们报告了五次自聚焦非线性以及一维谐波势中立方-五次 Gross Pitaeskii 方程（GPE）的直接解。 我们探讨了三维横向运动产生的五次非线性项对吸引和排斥原子间相互作用的理想一维纯雪茄状模型的影响在玻色-爱因斯坦凝聚（BEC）中。 此外，我们提供了一个闭合的解析表达式，用于评估仅考虑立方非线性 GPE 时描述一维 BEC 所产生的误差。 显示英文摘要

摘要： By means of new general variational method we report a direct solution for the quintic self-focusing nonlinearity and cubic-quintic 1D Gross Pitaeskii equation (GPE) in a harmonic confined potential. We explore the influence of the 3D transversal motion generating a quintic nonlinear term on the ideal 1D pure cigar-like shape model for the attractive and repulsive atom-atom interaction in Bose Einstein condensates (BEC). Also, we offer a closed analytical expression for the evaluation of the error produced when solely the cubic nonlinear GPE is considered for the description of 1D BEC.