Algebraic method for group classification of \((1+1)\)-dimensional linear Schrödinger equations

DOI10.1007/s10440-018-0169-yzbMath1409.35179arXiv1607.04118OpenAlexW2964148490MaRDI QIDQ1731114

Roman O. Popovych, Peter Basarab-Horwath, Célestin Kurujyibwami

Publication date: 20 March 2019

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.04118

zbMATH Keywords

Schrödinger equationsequivalence groupLie symmetrygroup classification of differential equationsgroup analysis of differential equationsequivalence groupoid

Mathematics Subject Classification ID

Geometric theory, characteristics, transformations in context of PDEs (35A30) Symmetries, invariants, etc. in context of PDEs (35B06) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (14)

Mapping method of group classification ⋮ Symmetries of Schrödinger–Pauli equations for charged particles and quasirelativistic Schrödinger equations ⋮ Equivalence and symmetries for variable coefficient linear heat type equations. I ⋮ Group analysis of general Burgers–Korteweg–de Vries equations ⋮ Equivalence groupoid and group classification of a class of variable-coefficient Burgers equations ⋮ Equivalence groupoids and group classification of multidimensional nonlinear Schrödinger equations ⋮ Abelian Lie symmetry algebras of two‐dimensional quasilinear evolution equations ⋮ Generalization of the algebraic method of group classification with application to nonlinear wave and elliptic equations ⋮ Lie symmetries of two-dimensional shallow water equations with variable bottom topography ⋮ Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein-Gordon equations ⋮ On the simplification of the form of Lie transformation groups admitted by systems of evolution differential equations ⋮ Exact solutions of Klein–Gordon equations in external electromagnetic fields on 3D de Sitter background ⋮ Enhanced symmetry analysis of two-dimensional Burgers system ⋮ Symmetries of Schrödinger equation with scalar and vector potentials

Cites Work

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