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Second and fourth Painlevé hierarchies and Jimbo-Miwa linear problems
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The relations between the different linear problems for Painlevé equations is an intriguing open problem. Here we consider our previously given second and fourth Painlevé hierarchies [Publ. Res. Inst. Math. Sci. (Kyoto) 37, 327–347 (2001)], and show that they could alternatively have been derived using the linear problems of Jimbo and Miwa. That is, we give a gauge transformation of our linear problems for these two hierarchies which maps those of the second and fourth Painlevé equations themselves onto those of Jimbo and Miwa.
Title: Second and fourth Painlevé hierarchies and Jimbo-Miwa linear problems
Description:
The relations between the different linear problems for Painlevé equations is an intriguing open problem.
Here we consider our previously given second and fourth Painlevé hierarchies [Publ.
Res.
Inst.
Math.
Sci.
(Kyoto) 37, 327–347 (2001)], and show that they could alternatively have been derived using the linear problems of Jimbo and Miwa.
That is, we give a gauge transformation of our linear problems for these two hierarchies which maps those of the second and fourth Painlevé equations themselves onto those of Jimbo and Miwa.
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