TY - JOUR
T1 - Proof of the dubrovin conjecture and analysis of the tritronquée solutions of PI
AU - Costin, O.
AU - Huang, M.
AU - Tanveer, S.
PY - 2014/3/15
Y1 - 2014/3/15
N2 - We show that the tritronquée solution yt of the Painlevé equation PI that behaves algebraically for large z with arg z = π/5 is analytic in a region containing the sector {z ≠0; arg z ∈[-3π/5,π]} and the disk {z: |z| <37=20}. This implies the Dubrovin conjecture, an important open problem in the theory of Painlevé transcendents. As a by-product, we obtain the value of the tritronquée and its derivative at zero, also important in applications, within less than 1/100 rigorous error bounds. © 2014.
AB - We show that the tritronquée solution yt of the Painlevé equation PI that behaves algebraically for large z with arg z = π/5 is analytic in a region containing the sector {z ≠0; arg z ∈[-3π/5,π]} and the disk {z: |z| <37=20}. This implies the Dubrovin conjecture, an important open problem in the theory of Painlevé transcendents. As a by-product, we obtain the value of the tritronquée and its derivative at zero, also important in applications, within less than 1/100 rigorous error bounds. © 2014.
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U2 - 10.1215/00127094-2429589
DO - 10.1215/00127094-2429589
M3 - RGC 21 - Publication in refereed journal
SN - 0012-7094
VL - 163
SP - 665
EP - 704
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 4
ER -