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arXiv · 2205.14873

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

A. Paliathanasis·G. Leon·P. G. L. Leach
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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.

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A. Paliathanasis, G. Leon, P. G. L. Leach. 2022-05-30. Lie symmetry classification and qualitative analysis for the fourth-order Schrödinger equation. https://arxiv.org/abs/2205.14873

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