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

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  • Kudryashov, Nikolai A.
  • Efimova, Olga Yu.

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=∞ are found by means of the power geometry method. 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.

Suggested Citation

  • Kudryashov, Nikolai A. & Efimova, Olga Yu., 2006. "Power expansions for solution of the fourth-order analog to the first Painlevé equation," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 110-124.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:1:p:110-124
    DOI: 10.1016/j.chaos.2005.08.196
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    Cited by:

    1. Kudryashov, Nikolai A., 2009. "Special polynomials associated with rational solutions of some hierarchies," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1447-1462.
    2. Demina, Maria V. & Kudryashov, Nikolai A., 2007. "The Yablonskii–Vorob’ev polynomials for the second Painlevé hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 526-537.

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