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On a generalization of the Chazy equation with a movable singular line

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Abstract

We generalize a third-order Chazy equation with a movable singular line, which has only negative resonances. For differential equations of order 2n+1 with resonances −1,−2, …, −(2n + 1), we study the convergence of the series representing their solutions, the existence of rational solutions, the invariance of these equations under certain transformations, and the existence of three-parameter solutions with a movable singular line.

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References

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Authors and Affiliations

  1. Grodno State University, Grodno, Belarus

    T. N. Van’kova & I. P. Martynov

Authors
  1. T. N. Van’kova
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  2. I. P. Martynov
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Additional information

Original Russian Text © T.N. Van’kova, I.P. Martynov, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45, No. 8, pp. 1085–1094.

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Van’kova, T.N., Martynov, I.P. On a generalization of the Chazy equation with a movable singular line. Diff Equat 45, 1105–1115 (2009). https://doi.org/10.1134/S0012266109080023

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  • DOI: https://doi.org/10.1134/S0012266109080023

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