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)
The Painlevé III equation and the Iwasawa decomposition. (English) Zbl 0827.35114
Summary: For the third Painlevé equation an explicit isomorphism between the monodromy data and the data of the approach of Dorfmeister-Pedit-Wu, based on the Iwasawa decomposition of the loop groups, is established. As an application, this provides a simple algebraic way to calculate the monodromy data in terms of the Cauchy data at zero.
35Q53KdV-like (Korteweg-de Vries) equations
53C45Global surface theory (convex surfaces à la A. D. Aleksandrov)
37J35Completely integrable systems, topological structure of phase space, integration methods
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
81R10Infinite-dimensional groups and algebras motivated by physics
[1]Bateman H., Erdelyi A.: Higher Transcendental Functions, vol.2 New-York: McGraw-Hill 1955
[2]Bobenko A.I.: Constant mean curvature surfaces and integrable equations, Uspekhi Matem. Nauk46(4), 3–42 (1991) (Russian). [English transl.: Russ. Math. Surv.46(4) (1991), 1–45]
[3]Deift P.A., Zhou, X.: A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation, Ann. of Math.137, 295–368 (1993) · Zbl 0771.35042 · doi:10.2307/2946540
[4]Dorfmeister J., Pedit F., Wu H.: Weierstrass type representations of harmonic maps into symmetric spaces, Preprint (1993)
[5]Flaschka H., Newell A.C.: Monodromy and spectrum preserving deformations I, Comm. Math. Phys.76, 67–116 (1980) · Zbl 0439.34005 · doi:10.1007/BF01197110
[6]Its A.R., Novokshenov V.Yu.: The isomonodromic deformation method in the theory of the Painlevé equations, Lect. Notes Math. 1191, Berlin Heidelberg New York: Springer 1986
[7]Jimbo T.: Monodromy problem and the boundary condition for some Painlevé equations, Publ. RIMS Kyoto Univ.18, 1137–1161 (1982) · Zbl 0535.34042 · doi:10.2977/prims/1195183300
[8]Krichever I.M.: Analogue of the D’Alambert formula for the equations of the principal chiral field and the sine-gordon equation, Dokl. Akad. Nauk SSSR253(2), 288–292 (1980) (Russian). [English transl. Sov. Math. Dokl22 (1981), 79–84]
[9]Lerner D., Sterling I.: Construction of constant mean curvature surfaces using the DPW representation of harmonic maps, SFB 288 Preprint No 92, Berlin (1993)
[10]McIntosh I.: Infinite dimensional Lie groups and the two-dimensional Toda lattice, in: Harmonic maps and integrable systems, ed: A.P. Fordy, J.C. Wood, Aspects of Mathematics E23, Wiesbaden: Vieweg 1994
[11]Novokshenov V.Yu: On the asymptotics of the general real-valued solution to the third Painlevé equation, Dokl. Akad. Nauk. SSSR283(5), 1161–1165 (1985) (Russian). [English transl. Sov. Phys. Dokl.30, (1985), 666–668]
[12]Pinkall U.: Fast loop group factorization and Mr. Bubble, Talk at the conference ”Differentialgeometrie and Quantenphysik”, Miedzyzdroje (1994)
[13]Presley A., Segal G.: Loop Groups, Oxford: Clarendon Press 1986