liu.seSearch for publications in DiVA
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • 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
Integrable perturbations of the harmonic oscillator and Poisson pencils
Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology.
2001 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 17, no 2, 191-209 p.Article in journal (Refereed) Published
Abstract [en]

Integrable perturbations of the two-dimensional harmonic oscillator are studied with the use of the recently developed theory of quasi-Lagrangian equations (equations of the form q¨ = A-1(q)?k(q) where A(q) is a Killing matrix) and with the use of Poisson pencils. A quite general class of integrable perturbations depending on an arbitrary solution of a certain second-order linear PDE is found in the case of harmonic oscillator with equal frequencies. For the case of nonequal frequencies all quadratic perturbations admitting two integrals of motion which are quadratic in velocities are found. A non-potential generalization of the Korteveg-de Vries integrable case of the Hénon-Heiles system is obtained. In the case when the perturbation is of a driven type (i.e. when one of the equations is autonomous) a method of solution of these systems by separation of variables and quadratures is presented.

Place, publisher, year, edition, pages
2001. Vol. 17, no 2, 191-209 p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-47425DOI: 10.1088/0266-5611/17/2/301OAI: oai:DiVA.org:liu-47425DiVA: diva2:268321
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13

Open Access in DiVA

No full text

Other links

Publisher's full text

Authority records BETA

Marciniak, Krzysztof

Search in DiVA

By author/editor
Marciniak, Krzysztof
By organisation
The Institute of TechnologyDepartment of Science and Technology
In the same journal
Inverse Problems
Engineering and Technology

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 348 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • 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