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)
A multi-component matrix loop algebra and a unified expression of the multi-component AKNS hierarchy and the multi-component BPT hierarchy. (English) Zbl 1222.37072
Summary: A set of multi-component matrix Lie algebras is constructed, which is devoted to obtaining a new loop algebra $\tilde A_{M-1}$. It follows that an isospectral problem is established. By making use of the Tu scheme [{\it G. Tu}, J. Math. Phys. 30, No. 2, 330--338 (1989; Zbl 0678.70015)], a Liouville integrable multi-component hierarchy of soliton equations is generated, which possesses the bi-Hamiltonian structures. As its reduction cases, the multi-component AKNS hierarchy and the formalism of the multi-component BPT hierarchy are given, respectively.

37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
17B80Applications of Lie algebras to integrable systems
Full Text: DOI
[1] Tu, G.: J. math. Phys.. 33, No. 2, 330 (1989)
[2] Ma, W.: Chin. J. Contemp. math.. 13, No. 1, 79 (1992)
[3] Hu, X.: J. phys. A. 27, 2497 (1994)
[4] Hu, X.: J. phys. A. 30, 619 (1997)
[5] Fan, E.: Physica A. 301, 105 (2002)
[6] Fan, E.: J. math. Phys.. 41, No. 11, 7769 (2000)
[7] Guo, F.: Acta math. Appl. sinica. 23, No. 2, 181 (2000)
[8] Guo, F.: J. systems sci. Math. sci.. 22, No. 1, 36 (2002)
[9] Zhang, Y.; Zhang, H.: J. math. Phys.. 43, No. 1, 466 (2002)
[10] Zhang, Y.: Phys. lett. A. 317, 280 (2003)
[11] Zhang, Y.; Yan, Q.: Chaos solitons fractals. 16, 263 (2003)
[12] Tsuchida, T.; Wadati, M.: Phys. lett. A. 257, 53 (1999)
[13] Ma, W.; Zhou, R.: Chin. ann. Math. B. 23, No. 3, 373 (2002)
[14] Guo, F.; Zhang, Y.: J. math. Phys.. 44, No. 12, 5793 (2003)