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

Abstract

The Lie symmetry analysis for the study of a $1+n$fourth-order Schrödinger 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 Schrödinger equation. Then, a qualitative analysis allows for the reduced ordinary differential equation to be analyzed to understand the asymptotic dynamics.

19 pages, no figures