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

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.

28 pages, 5 figures

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• Power and power-logarithmic expansions for travelling-wave solutions of the Burgers-Huxley equation