Power solution expansions of the analogue tothe first Painleve equation

2005/11/03 by Bruno, Aleksandr D., Kudryashov, Nikolai A.
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.nlin/0511008

Abstract

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=∞ are found. The exponential additions to the expansion of solution near z=∞ are computed. The obtained results confirm the hypothesis that the fourth-order analog of the first Painlevé equation determines new transcendental functions. By means of the methods of power geometry the basis of the plane lattice is also calculated.

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