A. V. Shapovalov, I. V. Shirokov, “Noncommutative integration of linear differential equations”, TMF, 104:2 (1995), 195–213; Theoret. and Math. Phys., 104:2 (1995), 921

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Teoreticheskaya i Matematicheskaya Fizika, 1995, Volume 104, Number 2, Pages 195–213 (Mi tmf1332)

This article is cited in 51 scientific papers (total in 51 papers)

Noncommutative integration of linear differential equations

A. V. Shapovalov^a, I. V. Shirokov^b

^a Tomsk State University
^b Omsk State University

Full-text PDF (1923 kB) Citations (51)

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Abstract: A method of noncommutative integration of linear partial differential equations that is analogous to noncommutative integration of finite-dimensional Hamiltonian systems is proposed. The method is based on the concept, introduced in the paper, of a

$\lambda$ representation of Lie algebras. The method can be applied to the integration of the Klein–Gordon equation in Riemannian spaces of non-Stäckel type (i. e., in spaces that do not admit complete separation of the variables).

Received: 17.05.1994

English version:
Theoretical and Mathematical Physics, 1995, Volume 104, Issue 2, Pages 921–934
DOI: https://doi.org/10.1007/BF02065973

Bibliographic databases:

Language: Russian

Citation: A. V. Shapovalov, I. V. Shirokov, “Noncommutative integration of linear differential equations”, TMF, 104:2 (1995), 195–213; Theoret. and Math. Phys., 104:2 (1995), 921–934

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf1332

https://www.mathnet.ru/eng/tmf/v104/i2/p195

This publication is cited in the following 51 articles:

A. A. Magazev, I. V. Shirokov, “On integrability of Klein-Gordon equations in electromagnetic fields invariant under subgroups of the Poincare group”, Russ Phys J, 2025
Eugene Oks, “Symmetry of the Non-Analytic Solution of the Dirac Equation Inside the Proton of Hydrogen Atoms”, Symmetry, 17:4 (2025), 517
Alexander I. Breev, Dmitry M. Gitman, Paulo A. Derolle, “Coherent states of an accelerated particle”, Eur. Phys. J. Plus, 139:10 (2024)
Alexander Shapovalov, Alexander Breev, “Harmonic Oscillator Coherent States from the Standpoint of Orbit Theory”, Symmetry, 15:2 (2023), 282
Alexander Breev, Dmitry Gitman, “New Exact Solutions Describing Quantum Asymmetric Top”, Symmetry, 15:2 (2023), 503
Obukhov V.V., “<P>Algebra of the Symmetry Operators of the Klein-Gordon-Fock Equation For the Case When Groups of Motions G(3) Act Transitively on Null Subsurfaces of Spacetime</P>”, Symmetry-Basel, 14:2 (2022), 346
Alexander Breev, Alexander Shapovalov, Dmitry Gitman, “Noncommutative Reduction of Nonlinear Schrödinger Equation on Lie Groups”, Universe, 8:9 (2022), 445
A. I. Breev, S. P. Gavrilov, D. M. Gitman, “Spinor Field Singular Functions in QED with Strong External Backgrounds”, J. Exp. Theor. Phys., 134:2 (2022), 157
Magazev A.A. Boldyreva M.N., “Schrodinger Equations in Electromagnetic Fields: Symmetries and Noncommutative Integration”, Symmetry-Basel, 13:8 (2021), 1527
Boldyreva M.N. Magazev A.A., “Exact Solutions of Klein-Gordon Equations in External Electromagnetic Fields on 3D de Sitter Background”, J. Math. Phys., 62:5 (2021), 053503
Obukhov V., “Separation of Variables in Hamilton-Jacobi and Klein-Gordon-Fock Equations For a Charged Test Particle in the Stackel Spaces of Type (1.1)”, Int. J. Geom. Methods Mod. Phys., 18:3 (2021), 2150036
M N Boldyreva, “Symmetry algebra of the time-dependent Schrödinger equation in constant and uniform fields”, J. Phys.: Conf. Ser., 1791:1 (2021), 012070
Ivanov D.A. Breev A.I., “Noncommutative Integration of the Klein-Gordon Equation in Electromagnetic Fields Admitting Functional Arbitrariness”, Russ. Phys. J., 62:12 (2020), 2169–2179
Obukhov V., “Separation of Variables in Hamilton-Jacobi Equation For a Charged Test Particle in the Stackel Spaces of Type (2.1)”, Int. J. Geom. Methods Mod. Phys., 17:14 (2020), 2050186
Breev A. Shapovalov A., “Non-Commutative Integration of the Dirac Equation in Homogeneous Spaces”, Symmetry-Basel, 12:11 (2020), 1867
Breev I A. Shapovalov V A., “Vacuum Quantum Effects on Lie Groups With Bi-Invariant Metrics”, Int. J. Geom. Methods Mod. Phys., 16:8 (2019), 1950122
Boldyreva M.N., Magazev A.A., “On the Lie Symmetry Algebras of the Stationary Schr?dinger and Pauli Equations”, Russ. Phys. J., 59:10 (2017), 1671–1680
Breev A.I., Magazev A.A., “Integration of the Dirac Equation on Lie Groups in An External Electromagnetic Field Admitting a Noncommutative Symmetry Algebra”, Russ. Phys. J., 59:12 (2017), 2048–2058
A. I. Breev, A. V. Shapovalov, “Noncommutative Integrability of the Klein–Gordon and Dirac Equations in (2+1)-Dimensional Spacetime”, Russ Phys J, 59:11 (2017), 1956
Breev A.I., Kozlov A.V., “Vacuum Averages of the Energy-Momentum Tensor of a Scalar Field in Homogeneous Spaces With a Conformal Metric”, Russ. Phys. J., 58:9 (2016), 1248–1257

Citing articles in Google Scholar: Russian citations, English citations
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