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Power expansions for solution of the fourth-order analog to the first Painlevé equation

Nikolai A. Kudryashov·Olga Yu. Efimova
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Abstract

One of the fourth-order analog to the first Painlevé equation is studied. All power expansions for solutions of this equation near points $z=0$ and $z=\infty$ are found by means of the power geometry method. The exponential additions to the expansion of solution near $z=\infty$ are computed. The obtained results confirm the hypothesis that the fourth-order analog of the first Painlevé equation determines new transcendental functions.

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Nikolai A. Kudryashov, Olga Yu. Efimova. 2005-07-14. Power expansions for solution of the fourth-order analog to the first Painlevé equation. https://doi.org/10.1016/j.chaos.2005.08.196

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