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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 206, Number 2, Pages 139–148
DOI: https://doi.org/10.4213/tmf9997 (Mi tmf9997) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Nonlocal symmetries of some nonlinear partial differential equations with third-order Lax pairs

Xiazhi Hao

College of Science, Zhejiang University of Technology, Hangzhou, China
Full-text PDF (381 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf9997
Abstract: By including spectral functions, we obtain nonlocal symmetries equivalent to Lie point symmetries of the corresponding extended systems for the Boussinesq equation, the modified generalized Vakhnenko equation, the Hirota–Satsuma equation, and the Sawada–Kotera equation. All considered equations have third-order Lax pairs, which allows studying their nonlocal symmetries in a unified way.
Keywords: nonlocal symmetry, Boussinesq equation, modified generalized Vakhnenko equation, Hirota–Satsuma equation, Sawada–Kotera equation.
Funding agency Grant number
Zhejiang Provincial Natural Science Foundation of China Q20A010009
General Scientific Research of Zhejiang Province 201909003329
National Natural Science Foundation of China 11675055
Natural Science Foundation of Shanghai 19ZR1414000
This research was supported by the Natural Science Foundation of Zhejiang Province (No. LQ20A010009), General Scientific Research of Zhejiang Province (No. 201909003329), National Natural Science Foundation of China (No. 11675055), and Natural Science Foundation of Shanghai (No. 19ZR1414000).
Received: 12.10.2020
Revised: 12.10.2020
English version:
Theoretical and Mathematical Physics, 2021, Volume 206, Issue 2, Pages 119–127
DOI: https://doi.org/10.1134/S004057792102001X
Bibliographic databases:
Document Type: Article
MSC: 34M45;76M60
Language: Russian
Citation: Xiazhi Hao, “Nonlocal symmetries of some nonlinear partial differential equations with third-order Lax pairs”, TMF, 206:2 (2021), 139–148; Theoret. and Math. Phys., 206:2 (2021), 119–127
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf9997
  • https://www.mathnet.ru/eng/tmf/v206/i2/p139
    • This publication is cited in the following 2 articles:
    1. W. Cui, Y. Liu, “Nonlocal symmetries and interaction solutions for the $(n + 1)$-dimensional generalized Korteweg–de Vries equation”, Phys. Scr., 98:4 (2023), 045204  crossref
    2. Y. Hu, F. Zhang, X. Xin, “Nonlocal symmetry, exact solutions and conservation laws of the (1+1)-dimensional Levi equation”, Comp. Appl. Math., 41:5 (2022)  crossref  mathscinet
    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
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    References:59
    First page:12
     
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