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Transformation that changes the geometric structure of a vector field

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Abstract

We propose a method of constructing vector fields with certain vortex properties by means of transformations that change the value of the field vector at every point, the form of the field lines, and their mutual position. We discuss and give concrete examples of the prospects of using the method in applications involving solution of partial differential equations, including nonlinear ones.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Division of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620219, Russia

    N. I. Chernykh & Yu. N. Subbotin

  2. Russian State Professional-Pedagogical University, ul. Mashinostroitelei 11, Yekaterinburg, 620012, Russia

    V. P. Vereshchagin

Authors
  1. N. I. Chernykh
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  2. Yu. N. Subbotin
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  3. V. P. Vereshchagin
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Corresponding author

Correspondence to N. I. Chernykh.

Additional information

Original Russian Text © N.I. Chernykh, Yu.N. Subbotin, V.P. Vereshchagin, 2009, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Vol. 15, No. 1.

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Chernykh, N.I., Subbotin, Y.N. & Vereshchagin, V.P. Transformation that changes the geometric structure of a vector field. Proc. Steklov Inst. Math. 266 (Suppl 1), 118–128 (2009). https://doi.org/10.1134/S0081543809060091

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  • DOI: https://doi.org/10.1134/S0081543809060091

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