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Algebraic Method for Group Classification of (1+1)-Dimensional Linear Schrodinger Equations
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering. Univ Rwanda, Rwanda.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
Wolfgang Pauli Inst, Austria; NAS Ukraine, Ukraine.
2018 (English)In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, Vol. 157, no 1, p. 171-203Article in journal (Refereed) Published
Abstract [en]

We carry out the complete group classification of the class of (1+1)-dimensional linear Schrodinger equations with complex-valued potentials. After introducing the notion of uniformly semi-normalized classes of differential equations, we compute the equivalence groupoid of the class under study and show that it is uniformly semi-normalized. More specifically, each admissible transformation in the class is the composition of a linear superposition transformation of the corresponding initial equation and an equivalence transformation of this class. This allows us to apply the new version of the algebraic method based on uniform semi-normalization and reduce the group classification of the class under study to the classification of low-dimensional appropriate subalgebras of the associated equivalence algebra. The partition into classification cases involves two integers that characterize Lie symmetry extensions and are invariant with respect to equivalence transformations.

Place, publisher, year, edition, pages
SPRINGER , 2018. Vol. 157, no 1, p. 171-203
Keywords [en]
Group classification of differential equations; Group analysis of differential equations; Equivalence group; Equivalence groupoid; Lie symmetry; Schrodinger equations
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-151473DOI: 10.1007/s10440-018-0169-yISI: 000443248300009OAI: oai:DiVA.org:liu-151473DiVA, id: diva2:1250677
Note

Funding Agencies|International Science Programme (ISP); East African Universities Mathematics Programme (EAUMP); Austrian Science Fund (FWF) [P25064]

Available from: 2018-09-24 Created: 2018-09-24 Last updated: 2018-09-24

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Kurujyibwami, CelestinBasarab-Horwath, Peter
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Mathematical Analysis

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