Mid Sweden University

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
Matrix solitons solutions of the modified Korteweg-de Vries equation.
Sapienza Università di Roma, Rome, Italy.
Sapienza Università di Roma, Rome, Italy.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education. Instytut Matematyki Uniwersytet Jana Kochanowskiego w Kielcach Kielce Poland.
2020 (English)In: Nonlinear Dynamics of Structures, Systems and Devices: Proceedings of the First International Nonlinear Dynamics Conference (NODYCON 2019) / [ed] W. Lacarbonara, B. Balachandran, J. Ma, J.A. Tenreiro Machado, and G. Stepan, Springer, 2020, Vol. I, p. 75-83Conference paper, Published paper (Refereed)
Abstract [en]

Nonlinear non-abelian Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations and their links via Bäcklund transformations are considered. The focus is on the construction of soliton solutions admitted by matrix modified Korteweg–de Vries equation. Matrix equations can be viewed as a specialisation of operator equations in the finite dimensional case when operators admit a matrix representation. Bäcklund transformations allow to reveal structural properties Carillo and Schiebold (J Math Phys 50:073510, 2009) enjoyed by non-commutative KdV-type equations, such as the existence of a recursion operator. Operator methods combined with Bäcklund transformations allow to construct explicit solution formulae Carillo and Schiebold (J Math Phys 52:053507, 2011). The latter are adapted to obtain solutions admitted by the 2 × 2 and 3 × 3 matrix mKdV equation. Some of these matrix solutions are visualised to show the solitonic behaviour they exhibit. A further key tool used to obtain the presented results is an ad hoc construction of computer algebra routines to implement non-commutative computations.

Place, publisher, year, edition, pages
Springer, 2020. Vol. I, p. 75-83
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:miun:diva-40823DOI: 10.1007/978-3-030-34713-0_8Scopus ID: 2-s2.0-85098616408ISBN: 978-3-030-34712-3 (print)OAI: oai:DiVA.org:miun-40823DiVA, id: diva2:1512771
Conference
NODYCON 2019
Available from: 2020-12-28 Created: 2020-12-28 Last updated: 2022-06-01Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records

Schiebold, Cornelia

Search in DiVA

By author/editor
Schiebold, Cornelia
By organisation
Department of Mathematics and Science Education
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar

doi
isbn
urn-nbn

Altmetric score

doi
isbn
urn-nbn
Total: 139 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