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On the internal approach to differential equations. 1. The involutiveness and standard basis

  • Veronika Chrastinová EMAIL logo and Václav Tryhuk
Published/Copyright: November 3, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 4

Abstract

The article treats the geometrical theory of partial differential equations in the absolute sense, i.e., without any additional structures and especially without any preferred choice of independent and dependent variables. The equations are subject to arbitrary transformations of variables in the widest possible sense. In this preparatory Part 1, the involutivity and the related standard bases are investigated as a technical tool within the framework of commutative algebra. The particular case of ordinary differential equations is briefly mentioned in order to demonstrate the strength of this approach in the study of the structure, symmetries and constrained variational integrals under the simplifying condition of one independent variable. In full generality, these topics will be investigated in subsequent Parts of this article.

MSC 2010: Primary 58A17; 58E99; Secondary 13E05
Keywords: higher-order symmetries; diffiety; involutivity

(Communicated by Andras Ronto)

References

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Received: 2013-12-22
Accepted: 2014-4-14
Published Online: 2016-11-3
Published in Print: 2016-8-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0198
Keywords for this article
higher-order symmetries; diffiety; involutivity

Articles in the same Issue

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  2. Effect algebras with a full set of states
  3. Research Article
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  5. Research Article
  6. On properties of the free BCI-algebra with one generator
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  9. Research Article
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  11. Research Article
  12. On skew-commuting mappings in semiprime rings
  13. Research Article
  14. On the subordination and superordination of strongly starlike functions
  15. Research Article
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  17. Research Article
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  44. Law of inertia for the factorization of cubic polynomials — the case of discriminants divisible by three
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