zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Quasi-linear Stokes phenomenon for the second Painlevé transcendent. (English) Zbl 1048.34146

The paper is devoted to the study of the quasi-linear Stokes phenomenon for the second Painlevé equation

y xx =2y 3 +xy-α

by using the Riemann-Hilbert approach. The main result is the precise description of the exponentially small jump of the dominant solution approaching α/x as |x| tends to infinity. The paper closes with the computation of the coefficient asymptotics for the asymptotic power expansion of the dominant solution.

34M40Stokes phenomena and connection problems (ODE in the complex domain)
34M50Inverse problems in theory of ODE in the complex domain (Riemann-Hilber, etc.)
34M55Painlevé and other special equations; classification, hierarchies