标题： 四阶薛定谔方程的李对称分类和定性分析 显示英文标题

标题： Lie symmetry classification and qualitative analysis for the fourth-order Schrödinger equation

摘要： 李对称性分析用于研究由存在最小长度时变形代数的修改所启发的$1+n~$四阶薛定谔方程。 具体而言，我们对存在非平凡李对称性的标量场势函数进行了详细的分类，并简化了薛定谔方程。 然后，定性分析使得可以对约化的常微分方程进行分析以理解渐近动力学。 显示英文摘要

摘要： The Lie symmetry analysis for the study of a $1+n~$fourth-order Schr\"{o}dinger equation inspired by the modification of the deformation algebra in the presence of a minimum length is applied. Specifically, we perform a detailed classification for the scalar field potential function where non-trivial Lie symmetries exist and simplify the Schr\"{o}dinger equation. Then, a qualitative analysis allows for the reduced ordinary differential equation to be analyzed to understand the asymptotic dynamics.