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Lie symmetry classification and qualitative analysis for the fourth-order Schrödinger equation (2205.14873v1)
Published 30 May 2022 in math-ph, math.AP, and math.MP
Abstract: 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.