Lie Symmetry Classification and Qualitative Analysis for the Fourth-Order Schrödinger Equation

Andronikos Paliathanasis (), Genly Leon and Peter G. L. Leach
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Andronikos Paliathanasis: Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa
Genly Leon: Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa
Peter G. L. Leach: Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa

Mathematics, 2022, vol. 10, issue 17, 1-15

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 analysed to understand the asymptotic dynamics.

Keywords: Lie symmetries; invariants; fourth-order Schrödinger equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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