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, 2023, Volume 214, Number 2, Pages 224–238
DOI: https://doi.org/10.4213/tmf10347 (Mi tmf10347) 		 
Noncommutative generalization and quasi-Gramian solutions of the Hirota equation

H.  Wajahat  A. Riaz

School of Science, China University of Mining and Technology, Beijing, China
Full-text PDF (735 kB)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tmf10347
Abstract: The nonlinear Schrödinger (NLS) and modified Korteweg–de Vries (mKdV) equations can be combined to form an integrable equation known as the Hirota equation. In this paper, we investigate a noncommutative generalization of the Hirota equation by establishing the zero-curvature condition, identifying the Lax pair, and using the covariance strategy to find the binary Darboux transformation (DT) and the Darboux transformation (DT) for the noncommutative Hirota equation. We also construct the quasi-Gramian solutions. First-order single- and double-peaked solutions in noncommutative contexts are also presented.
Keywords: noncommutative integrable system, Darboux transformation, binary Darboux transformation, soliton.
Funding agency Grant number
National Natural Science Foundation of China 11871471
11331008
11931017
Foreign Experts Scientific Cooperation Fund
This work was supported by the National Natural Science Foundation of China (grant Nos. 11871471, 11331008, and 11931017) and the Foreign Experts Scientific Cooperation Fund.
Received: 07.08.2022
Revised: 15.09.2022
English version:
Theoretical and Mathematical Physics, 2023, Volume 214, Issue 2, Pages 194–206
DOI: https://doi.org/10.1134/S0040577923020046
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: H.  Wajahat  A. Riaz, “Noncommutative generalization and quasi-Gramian solutions of the Hirota equation”, TMF, 214:2 (2023), 224–238; Theoret. and Math. Phys., 214:2 (2023), 194–206
Citation in format AMSBIB
\Bibitem{Ria23}
\by H.~~Wajahat~~A.~Riaz
\paper Noncommutative generalization and quasi-Gramian solutions of the~Hirota equation
\jour TMF
\yr 2023
\vol 214
\issue 2
\pages 224--238
\mathnet{http://mi.mathnet.ru/tmf10347}
\crossref{https://doi.org/10.4213/tmf10347}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4563403}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2023TMP...214..194R}
\transl
\jour Theoret. and Math. Phys.
\yr 2023
\vol 214
\issue 2
\pages 194--206
\crossref{https://doi.org/10.1134/S0040577923020046}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85149261539}
Linking options:
  • https://www.mathnet.ru/eng/tmf10347
  • https://doi.org/10.4213/tmf10347
  • https://www.mathnet.ru/eng/tmf/v214/i2/p224
    • 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
    Statistics & downloads:
    Abstract page:130
    Full-text PDF :10
    Russian version HTML:89
    References:19
    First page:3
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024