Teoreticheskaya i Matematicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


TMF:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Teoreticheskaya i Matematicheskaya Fizika, 2025, Volume 222, Number 1, Pages 122–135
DOI: https://doi.org/10.4213/tmf10752 (Mi tmf10752) 		 
Nonlocal symmetries of the Degasperis–Procesi equation

Xiaoyong Li, Changzheng Qu

School of Mathematics and Statistics, Ningbo University, Ningbo, China
Full-text PDF (468 kB) First page
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf10752
Abstract: We study nonlocal symmetries of the Degasperis–Procesi equation, which are shown to be closely related to its integrable structure. First, applying the Hamiltonian operator to the gradients of the spectral parameter, we construct nonlocal symmetries of the Kaup–Kupershmidt equation. Next, we show that the nonlocal symmetries can be prolonged to local symmetries for a prolonged system by introducing new dependent variables. Finally, applying the Liouville transformation relating the Degasperis–Procesi and Kaup–Kupershmidt hierarchies, we obtain the corresponding nonlocal symmetries of the Degasperis–Procesi equation.
Keywords: nonlocal symmetry, Hamiltonian operator, Liouville transformation, Degasperis–Procesi equation, Kaup–Kupershmidt equation.
Funding agency Grant number
National Natural Science Foundation of China 12431008
K. C. Wong Magna Fund (Ningbo University)
The work of Xiaoyong Li was supported by the National Natural Science Foundation of China under grant No. 12431008 and K. C. Wong Magna Fund in Ningbo University. The work of Changzheng Qu was supported by the National Natural Science Foundation of China (grant No. 12431008).
Received: 07.05.2024
Revised: 07.09.2024
Published: 16.01.2025
English version:
Theoretical and Mathematical Physics, 2025, Volume 222, Issue 1, Pages 106–118
DOI: https://doi.org/10.1134/S0040577925010088
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Xiaoyong Li, Changzheng Qu, “Nonlocal symmetries of the Degasperis–Procesi equation”, TMF, 222:1 (2025), 122–135; Theoret. and Math. Phys., 222:1 (2025), 106–118
Citation in format AMSBIB
\Bibitem{LiQu25}
\by Xiaoyong~Li, Changzheng~Qu
\paper Nonlocal symmetries of the~Degasperis--Procesi equation
\jour TMF
\yr 2025
\vol 222
\issue 1
\pages 122--135
\mathnet{http://mi.mathnet.ru/tmf10752}
\crossref{https://doi.org/10.4213/tmf10752}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4855375}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2025TMP...222..106L}
\transl
\jour Theoret. and Math. Phys.
\yr 2025
\vol 222
\issue 1
\pages 106--118
\crossref{https://doi.org/10.1134/S0040577925010088}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-86000244770}
Linking options:
  • https://www.mathnet.ru/eng/tmf10752
  • https://doi.org/10.4213/tmf10752
  • https://www.mathnet.ru/eng/tmf/v222/i1/p122
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025