Differential equations on manifolds and Lie algebras

In this paper, we are starting to develop an algebraic approach to differential equations on smooth manifolds. As a first step, we present a general scheme of this approach, in which the planar case essentially coincides with the traditional formalism of partial differential equations.

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Publication Details

Journal
Theoretical and Mathematical Physics
Published
2026-03-01
DOI
https://doi.org/10.1134/s0040577926030013
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
article
Field-Weighted Citation Impact
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article

Differential equations on manifolds and Lie algebras

V. V. Zharinov
Theoretical and Mathematical Physics
Homotopy and Cohomology in Algebraic Topology
article

Differential equations on manifolds and Lie algebras

V. V. Zharinov
article en

Abstract

In this paper, we are starting to develop an algebraic approach to differential equations on smooth manifolds. As a first step, we present a general scheme of this approach, in which the planar case essentially coincides with the traditional formalism of partial differential equations.

Theoretical and Mathematical PhysicsVol. 226(3)
Russian Academy of Sciences (RU), Steklov Mathematical Institute (RU)
Openalex Percentile: Top 7%
Homotopy and Cohomology in Algebraic Topology
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Differential equations on manifolds and Lie algebras — V. V. Zharinov · Theoretical and Mathematical Physics (2026) | TGRS Research Map | TGRS