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

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

2005-07-14

arxiv.org/abs/nlin/0507026v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

28 pages, 5 figures

Scientific paper

One of the fourth-order analog to the first Painlev\'{e} 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 Painlev\'{e} equation determines new transcendental functions.

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