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Power and non-power expansions of the solutions for the fourth-order analogue to the second Painlevé equation

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  • Demina, Maria V.
  • Kudryashov, Nikolai A.

Abstract

Fourth-order analogue to the second Painlevé equation is studied. This equation has its origin in the modified Korteveg–de Vries equation of the fifth-order when we look for its self-similar solution. All power and non-power expansions of the solutions for the fourth-order analogue to the second Painlevé equation near points z=0 and z=∞ are found by means of the power geometry method. The exponential additions to solutions of the equation studied are determined. Comparison of the expansions found with those of the six Painlevé equations confirm the conjecture that the fourth-order analogue to the second Painlevé equation defines new transcendental functions.

Suggested Citation

  • Demina, Maria V. & Kudryashov, Nikolai A., 2007. "Power and non-power expansions of the solutions for the fourth-order analogue to the second Painlevé equation," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 124-144.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:1:p:124-144
    DOI: 10.1016/j.chaos.2005.10.079
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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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