miun.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Noncommutative Korteweg-de Vries and modified Korteweg-de Vries hierarchies via recursion methods
Universita Roma La Sapienza.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
2009 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 7, article id 073510Article in journal (Refereed) Published
Abstract [en]

Here, noncommutative hierarchies of nonlinear equations are studied. They represent a generalization to the operator level of corresponding hierarchies of scalar equations, which can be obtained from the operator ones via a suitable projection. A key tool is the application of Baumlcklund transformations to relate different operator-valued hierarchies. Indeed, in the case when hierarchies in 1+1-dimensions are considered, a "Baumlcklund chart" depicts links relating, in particular, the Korteweg-de Vries (KdV) to the modified KdV (mKdV) hierarchy. Notably, analogous links connect the hierarchies of operator equations. The main result is the construction of an operator soliton solution depending on an infinite-dimensional parameter. To start with, the potential KdV hierarchy is considered. Then Baumlcklund transformations are exploited to derive solution formulas in the case of KdV and mKdV hierarchies. It is remarked that hierarchies of matrix equations, of any dimension, are also incorporated in the present framework.

Place, publisher, year, edition, pages
2009. Vol. 50, no 7, article id 073510
Keywords [en]
Korteweg-de Vries equation; mathematical operators; matrix algebra; nonlinear differential equations; solitons
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-9596DOI: 10.1063/1.3155080ISI: 000268614500029Scopus ID: 2-s2.0-68749111018OAI: oai:DiVA.org:miun-9596DiVA, id: diva2:233424
Available from: 2009-09-01 Created: 2009-09-01 Last updated: 2017-12-13Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records BETA

Schiebold, Cornelia

Search in DiVA

By author/editor
Schiebold, Cornelia
By organisation
Department of Natural Sciences, Engineering and Mathematics
In the same journal
Journal of Mathematical Physics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 136 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf