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Symmetry and first integrals of first-order system of differential equations

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Abstract

The defining equation is constructed for an algebra of infinitesimal Lie-symmetry-group operators of a first-order system of ordinary differential equations; some properties of the algebra are formulated; and the relation of the algebra with conservation laws is discussed. A similar approach is applied to a Hamilton system of general form.

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Literature cited

  1. E. Goursat, Lecons sur la Probleme de Kaff, Paris (1922).

  2. A. Poincare, Selected Works [Russian translation], Vol. 2, Nauka, Moscow (1972), p. 11.

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Authors and Affiliations

  1. Kalmytsk State University, USSR

    V. N. Shapovalov

Authors
  1. V. N. Shapovalov
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 53–56, February, 1977.

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Shapovalov, V.N. Symmetry and first integrals of first-order system of differential equations. Soviet Physics Journal 20, 181–184 (1977). https://doi.org/10.1007/BF01297380

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  • DOI: https://doi.org/10.1007/BF01297380

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