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Reduction of multidimensional first order equations with multi-homogeneous function of derivatives

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Abstract

We present an analysis of solutions to multidimensional first order equation order with several independent variables under assumption that the nonlinear part of the equation is a multi-homogeneous function of derivatives. The reduction of the original equation is performed for the class of solutions depending on linear combinations of prescribed groups of initial variables. We obtain solutions to the reduced equation. We consider also the cases of additional, multiplicational and combined separation of variables.

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References

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Authors and Affiliations

  1. Nizhni Novgorod State University, pr. Gagarina 23, Nizhni Novgorod, 603950, Russia

    I. V. Rakhmelevich

Authors
  1. I. V. Rakhmelevich
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Correspondence to I. V. Rakhmelevich.

Additional information

Original Russian Text © I.V. Rakhmelevich, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 4, pp. 57–67.

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Rakhmelevich, I.V. Reduction of multidimensional first order equations with multi-homogeneous function of derivatives. Russ Math. 60, 47–55 (2016). https://doi.org/10.3103/S1066369X16040071

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  • DOI: https://doi.org/10.3103/S1066369X16040071

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