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Representing Invertible Linear Differential Operators as the Composition of Triangular Ones

  • PARTIAL DIFFERENTIAL EQUATIONS
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Abstract

We study invertible linear differential operators in two variables. The problem of their description is relevant due to its connection with the problems of transformation of systems of partial differential equations. In the paper, we use algebraic methods of the theory of spectral sequences of chain complexes. It is proved that any invertible linear differential operator with two independent variables in the direct sum with the identity mapping can be represented as the composition of at most four triangular invertible operators. An algorithm of expansion into such a composition is formulated and demonstrated by an example.

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Funding

This work was financially supported by the Ministry of Science and Higher Education of the Russian Federation, project no. 0705-2020-0047 and the Russian Foundation for Basic Research, projects nos. 19-07-00817 and 20-07-00279).

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Moscow, 105005, Russia

    V. N. Chetverikov

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  1. V. N. Chetverikov
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Correspondence to V. N. Chetverikov.

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Translated by V. Potapchouck

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Chetverikov, V.N. Representing Invertible Linear Differential Operators as the Composition of Triangular Ones. Diff Equat 57, 1372–1381 (2021). https://doi.org/10.1134/S0012266121100116

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  • DOI: https://doi.org/10.1134/S0012266121100116

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