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)
On the multi-component NLS type equations on symmetric spaces: reductions and soliton solutions. (English) Zbl 1079.53075
Mladenov, Ivaïlo M.(ed.) et al., Proceedings of the 6th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 3--10, 2004. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-9-5/pbk). 203-217 (2005).
This is an introductory survey on multi-component nonlinear Schrödinger equations related to simple Lie algebras and symmetric spaces. These generalizations of the nonlinear Schrödinger equation were proposed by Fordy and Kulish in the early 1990’s. Recently, the authors sytematically studied these equations, their reductions and soliton solutions [Inverse Probl. 17, No. 4, 999--1015 (2001; Zbl 0988.35143) and J. Phys. A, Math. Gen. 34, No. 44, 9425--9461 (2001; Zbl 1001.37074)]. In particular, some of their results on this subject are reviewed and discussed in this paper. For the entire collection see [Zbl 1066.53003].

35Q55NLS-like (nonlinear Schrödinger) equations
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
37K30Relations of infinite-dimensional systems with algebraic structures
53C35Symmetric spaces (differential geometry)
35Q51Soliton-like equations