A Hirota bilinear equation for Painlevé transcendents PIV, PII and PI
2018 ◽
Vol 07
(04)
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pp. 1840001
Keyword(s):
We present some observations on the tau-function for the fourth Painlevé equation. By considering a Hirota bilinear equation of order four for this tau-function, we describe the general form of the Taylor expansion around an arbitrary movable zero. The corresponding Taylor series for the tau-functions of the first and second Painlevé equations, as well as that for the Weierstrass sigma function, arise naturally as special cases, by setting certain parameters to zero.
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2019 ◽
Vol 74
◽
pp. 184-198
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Keyword(s):
2018 ◽
Vol 75
(3)
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pp. 957-964
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Keyword(s):
2020 ◽
Vol 15
◽
pp. 61
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2016 ◽
Vol 72
(5)
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pp. 1225-1229
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Keyword(s):
2019 ◽
Vol 98
◽
pp. 184-190
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Keyword(s):
2020 ◽
Vol 25
(4)
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pp. 383-391
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