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Shimomura, Shun

Corrigendum to: “Elliptic asymptotic representation of the fifth Painlevé transcendents”. (English) Zbl 1528.34072

Kyushu J. Math. 77, No. 1, 191-202 (2023).
Summary: Our paper [ibid. 76, No. 1, 43–99 (2022; Zbl 1505.34131)] contains an incorrect Stokes graph. The amendment to the Stokes graph replaces the phase shifts of asymptotic solutions in the main theorems.

MSC:

34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies
34M56 Isomonodromic deformations for ordinary differential equations in the complex domain
34M30 Asymptotics and summation methods for ordinary differential equations in the complex domain
33E17 Painlevé-type functions

Keywords:

elliptic asymptotic representation; fifth Painlevé transcendents; Boutroux ansatz; WKB analysis; isomonodromy deformation; monodromy data; Jacobi elliptic functions; \(\vartheta\)-function

Citations:

Zbl 1505.34131
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Full Text: DOI

References:

[1] F. V. Andreev. On some special functions of the fifth Painlevé equation. (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 243 (1997), Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funktsii. 28, 10-18, 338; translation in J. Math. Sci. 99 (2000), 802-807. · Zbl 0907.34007
[2] F. V. Andreev and A. V. Kitaev. Connection formulae for asymptotics of the fifth Painlevé transcendent on the real axis. Nonlinearity 13 (2000), 1801-1840. · Zbl 0970.34076
[3] A. S. Fokas, A. R. Its, A. A. Kapaev and V. Yu. Novokshenov. Painlevé Transcendents, The Riemann-Hilbert Approach (Math Surveys and Monographs, 128). American Mathematical Society, Providence, RI, 2006. · Zbl 1111.34001
[4] A. V. Kitaev. The justification of asymptotic formulas that can be obtained by the method of isomonodromic deformations. (Russian) Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 179 (1989), Mat. Vopr. Teor. Rasprostr. Voln. 19, 101-109, 189-190; translation in J. Soviet Math. 57(3) (1991), 3131- 3135. · Zbl 0745.34061
[5] A. V. Kitaev. Elliptic asymptotics of the first and second Painlevé transcendents. (Russian) Uspekhi Mat. Nauk 49 (1994), 77-140; translation in Russian Math. Surveys 49 (1994), 81-150. · Zbl 0829.34040
[6] S. Shimomura. Elliptic asymptotic representation of the fifth Painlevé transcendents. Kyushu J. Math. 76 (2022), 43-99. · Zbl 1505.34131
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