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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 163, Number 2, Pages 277–287
DOI: https://doi.org/10.4213/tmf6499 (Mi tmf6499) 		 
This article is cited in 8 scientific papers (total in 8 papers)

A limit symmetry of the Korteweg–de Vries equation and its applications

Zhang Da-juna, Jian-bing Zhangba, Qing Shena

a Department of Mathematics, Shanghai University, Shanghai, China
b School of Mathematics Science, Xuzhou Normal University, Xuzhou, China
Full-text PDF (881 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf6499
Abstract: We discuss a symmetry of the Korteweg–de Vries (KdV) equation. This symmetry can be related to the squared eigenfunction symmetry by a limit procedure. As applications, we consider the similarity reduction of the KdV equation and a KdV equation with new self-consistent sources. We derive some solutions via a bilinear approach.
Keywords: symmetry, KdV equation, symmetry constraint, self-consistent source, bilinear method.
Received: 29.09.2009
English version:
Theoretical and Mathematical Physics, 2010, Volume 163, Issue 2, Pages 634–643
DOI: https://doi.org/10.1007/s11232-010-0046-y
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Zhang Da-jun, Jian-bing Zhang, Qing Shen, “A limit symmetry of the Korteweg–de Vries equation and its applications”, TMF, 163:2 (2010), 277–287; Theoret. and Math. Phys., 163:2 (2010), 634–643
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6499
  • https://www.mathnet.ru/eng/tmf/v163/i2/p277
    • This publication is cited in the following 8 articles:
    1. Gaizhu Qu, Junyang Zhang, Xiaorui Hu, Shoufeng Shen, “Limit solutions of loop solitons for a compound WKI-SP equation”, Applied Mathematics Letters, 163 (2025), 109452  crossref
    2. Tian H.-j., Feng X.-j., Liu W.-m., “Extended Kdv Equations Generated By Squared Eigenfunction Symmetry”, Appl. Math. Lett., 128 (2022), 107852  crossref  mathscinet  isi
    3. Chen K. Zhang Ch. Zhang D.-j., “Squared Eigenfunction Symmetry of the D Delta Mkp Hierarchy and Its Constraint”, Stud. Appl. Math., 147:2 (2021), 752–791  crossref  mathscinet  isi
    4. Wang X. Wang L., “Soliton, Breather and Rogue Wave Solutions For the Nonlinear Schrodinger Equation Coupled to a Multiple Self-Induced Transparency System”, Chin. Phys. Lett., 35:3 (2018), 030201  crossref  isi  scopus
    5. Zhang D.-J. Zhao S.-L. Sun Y.-Y. Zhou J., “Solutions To the Modified Korteweg-de Vries Equation”, Rev. Math. Phys., 26:7 (2014), 1430006  crossref  mathscinet  zmath  isi  scopus
    6. Sun Ying-Ying Yuan Juan-Ming Zh.D.-J., “Solutions To the Complex Korteweg-de Vries Equation: Blow-Up Solutions and Non-Singular Solutions”, Commun. Theor. Phys., 61:4 (2014), 415–422  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Xu D.-d. Zhang D.-j. Zhao S.-l., “The Sylvester Equation and Integrable Equations: i. the Korteweg-de Vries System and sine-Gordon Equation”, J. Nonlinear Math. Phys., 21:3 (2014), 382–406  crossref  mathscinet  isi  scopus
    8. Zhang Jian-Bing, Ji Jie, Shen Qing, Zhang Da-Jun, “A Limit Symmetry of Modified KdV Equation and Its Applications”, Commun Theor Phys (Beijing), 55:6 (2011), 960–964  crossref  mathscinet  zmath  adsnasa  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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