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Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 117, 14 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.117
(Mi sigma1416)
 

Truncated Solutions of Painlevé Equation $\mathrm{P_V}$

Rodica D. Costin

The Ohio State University, 231 W 18th Ave, Columbus, OH 43210, USA
References:
Abstract: We obtain convergent representations (as Borel summed transseries) for the five one-parameter families of truncated solutions of the fifth Painlevé equation with nonzero parameters, valid in half planes, for large independent variable. We also find the position of the first array of poles, bordering the region of analyticity. For a special value of this parameter they represent tri-truncated solutions, analytic in almost the full complex plane, for large independent variable. A brief historical note, and references on truncated solutions of the other Painlevé equations are also included.
Keywords: Painlevé trascendents; the fifth Painlevé equation; truncated solutions; poles of truncated solutions.
Received: May 1, 2018; in final form October 25, 2018; Published online October 31, 2018
Bibliographic databases:
Document Type: Article
MSC: 33E17; 34M30; 34M25
Language: English
Citation: Rodica D. Costin, “Truncated Solutions of Painlevé Equation $\mathrm{P_V}$”, SIGMA, 14 (2018), 117, 14 pp.
Citation in format AMSBIB
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\paper Truncated Solutions of Painlev\'e Equation $\mathrm{P_V}$
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\papernumber 117
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