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Reduction and noncommutative integration of linear differential equations

Abstract

A new method is proposed for derivation of exactly integrable linear differential equations based on the theory of noncommutative integration. The equations are obtained by reduction from original equations which are integrable in the noncommutative sense, with a large number of independent variables. It is shown that the reduced equations cannot be solved by traditional methods, since they do not possess the required algebraic symmetry.

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Additional information

V. V. Kuibyshev Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 55–60, November, 1993.

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Drokin, A.A., Shapovalov, A.V. & Shirokov, I.V. Reduction and noncommutative integration of linear differential equations. Russ Phys J 36, 1059–1063 (1993). https://doi.org/10.1007/BF00560445

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Keywords

  • Differential Equation
  • Traditional Method
  • Original Equation
  • Linear Differential Equation
  • Noncommutative Integration