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)
Numerical studies of the fourth Painlevé equation. (English) Zbl 0782.65099
The authors investigate numerically solutions of a special case of the fourth Painlevé equation $d\sp 2\eta/d\xi\sp 2 = 3\eta\sp 5 + 2\xi\eta\sp 3 + ((1/4)\xi\sp 2 -\nu-1/2)\eta$ with $\nu$ a parameter, satisfying the boundary condition $\eta(\xi)\to 0$ as $\xi\to + \infty$. The equation arises as a symmetric reduction of the derivative Schrödinger equation, which is a completely integrable soliton equation solvable by inverse scattering techniques. A numerical approach to describe the solution of the equation for noninteger $\nu$ is adopted, and information is obtained characterizing connection formulae which describe how the asymptotic behaviour of solutions as $\xi \to +\infty$ relates to that as $\xi \to -\infty$. A typical result shows the solution blows up whenever $\nu < -1$.

65L10Boundary value problems for ODE (numerical methods)
34B30Special ODE (Mathieu, Hill, Bessel, etc.)
34B15Nonlinear boundary value problems for ODE
Full Text: DOI