In this paper, we investigate a five-component Gross–Pitaevskii equation, which is demonstrated to describe the dynamics of an spinor Bose–Einstein condensate in one dimension. By employing the Hirota method with an auxiliary function, we obtain the explicit bright one- and two-soliton solutions for the equation via symbolic computation. With the choice of polarization parameter and spin density, the one-soliton solutions are divided into four types: one-peak solitons in the ferromagnetic and cyclic states and one- and two-peak solitons in the polar states. For the former two, solitons share the similar shape of one peak in all components. Solitons in the polar states have the one- or two-peak profiles, and the separated distance between two peaks is inversely proportional to the value of polarization parameter. Based on the asymptotic analysis, we analyze the collisions between two solitons in the same and different states.

中文翻译：

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转子Bose-Einstein凝聚物中多组分Gross-Pitaevskii方程的孤子解和碰撞

在本文中，我们研究了一个由五部分组成的Gross–Pitaevskii方程，该方程被证明可以描述一个 旋量玻色－爱因斯坦一维凝结。通过使用带有辅助函数的Hirota方法，我们通过符号计算获得了方程的显式明亮的一孤子和二孤子解。通过选择极化参数和自旋密度，单孤子解可分为四种类型：铁磁和循环态的一峰孤子和极化态的一峰和两峰孤子。对于前两个，孤子在所有分量中共享一个峰的相似形状。处于极性状态的孤子具有一个或两个峰的轮廓，并且两个峰之间的分隔距离与偏振参数的值成反比。基于渐近分析，我们分析了处于相同状态和不同状态的两个孤子之间的碰撞。