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A differential-geometric criterion of the kinematic integrability of nonlinear differential equations

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Abstract

A theorem on the existence of a G-representation and a differential-geometric criterion of the kinematic integrability for nonlinear differential equations from the Λ2-G-classes is proved. Examples of zero-curvature representations and metrics for some equations of mathematical physics are presented.

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References

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Authors and Affiliations

  1. Moscow State University, Russia

    D. V. Tikhomirov

  2. Finance Academy under the Government of the Russian Federation, Russia

    S. A. Zadadaev

Authors
  1. D. V. Tikhomirov
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  2. S. A. Zadadaev
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Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry, 2005.

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Tikhomirov, D.V., Zadadaev, S.A. A differential-geometric criterion of the kinematic integrability of nonlinear differential equations. J Math Sci 141, 1075–1080 (2007). https://doi.org/10.1007/s10958-007-0035-3

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  • DOI: https://doi.org/10.1007/s10958-007-0035-3

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