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Asymptotic Expansions of Solutions to the Second Term of the Fourth Painlevé Hierarchy

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Abstract

Asymptotic behavior and asymptotic expansions of solutions to the second term of the fourth Painlevé hierarchy are constructed using power geometry methods [1]. Only results for the case of general position—for the equation parameters \(\beta ,\delta \ne 0\)—are provided. For constructing asymptotic expansions, a code written in a computer algebra system is used.

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REFERENCES

  1. Pickering, A., Painlevé hierarchies and the Painlevé test, Theor. Math. Phys., 2003, vol. 137, no. 3, pp. 1733–1742.

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  2. Kudryashov, N.A., On the Fourth Painlevé Hierarchy, Theor. Math. Phys., 2003, vol. 134, no. 1, pp. 86–93.

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Funding

This work was supported by the Russian Science Foundation, project no. 19-71-10003.

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Authors and Affiliations

  1. National Research University—Higher School of Economics, 123458, Moscow, Russia

    V. I. Anoshin, A. D. Beketova, A. V. Parusnikova & K. V. Romanov

Authors
  1. V. I. Anoshin
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  2. A. D. Beketova
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  3. A. V. Parusnikova
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  4. K. V. Romanov
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Corresponding authors

Correspondence to V. I. Anoshin, A. D. Beketova, A. V. Parusnikova or K. V. Romanov.

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Translated by A. Klimontovich

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Anoshin, V.I., Beketova, A.D., Parusnikova, A.V. et al. Asymptotic Expansions of Solutions to the Second Term of the Fourth Painlevé Hierarchy. Program Comput Soft 48, 30–35 (2022). https://doi.org/10.1134/S0361768822010029

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  • DOI: https://doi.org/10.1134/S0361768822010029

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