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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 134, Number 1, Pages 74–84
DOI: https://doi.org/10.4213/tmf141 (Mi tmf141) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Classical Symmetry Reductions of the Schwarz–Korteweg–de Vries Equation in 2+12+1 Dimensions

M. L. Gandarias, M. S. Bruzón, J. Ramíres

Universidad de Cadiz
Full-text PDF (653 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf141
Abstract: Classical reductions of a (2+1)(2+1)-dimensional integrable Schwarz–Korteweg–de Vries equation are classified. These reductions to systems of partial differential equations in 1+11+1 dimensions admit symmetries that lead to further reductions, i.e., to systems of ordinary differential equations. All these systems have been reduced to second-order ordinary differential equations. We present some particular solutions involving two arbitrary functions.
Keywords: partial differential equations, Lie symmetries.
English version:
Theoretical and Mathematical Physics, 2003, Volume 134, Issue 1, Pages 62–71
DOI: https://doi.org/10.1023/A:1021867622943
Bibliographic databases:
Language: Russian
Citation: M. L. Gandarias, M. S. Bruzón, J. Ramíres, “Classical Symmetry Reductions of the Schwarz–Korteweg–de Vries Equation in 2+12+1 Dimensions”, TMF, 134:1 (2003), 74–84; Theoret. and Math. Phys., 134:1 (2003), 62–71
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf141
  • https://doi.org/10.4213/tmf141
  • https://www.mathnet.ru/eng/tmf/v134/i1/p74
    • This publication is cited in the following 7 articles:
    1. Farrukh Shehzad, Aly R. Seadawy, Sarfaraz Ahmed, Syed T. R. Rizvi, “Mathematical modeling and component generalization of (2+1)-dimensional Schwarz–Kortweg–de Vries model in shallow water waves”, Mod. Phys. Lett. B, 2024  crossref
    2. Weifang Liu, Cewen Cao, Xiao Yang, Xiaoxue Xu, “The (2+1)‐dimensional Schwarzian Korteweg–de Vries equation and its generalizations with discrete Lax matrices”, Math Methods in App Sciences, 2024  crossref
    3. Sarfaraz Ahmed, Aly R. Seadawy, Syed T. R. Rizvi, Umar Raza, “Multi-Peak and Propagation Behavior of M-Shape Solitons in (2 + 1)-Dimensional Integrable Schwarz-Korteweg-de Vries Problem”, Fractal Fract, 7:10 (2023), 709  crossref
    4. Li X. Zhang M., “Darboux Transformation and Soliton Solutions of the (2+1)-Dimensional Schwarz-Korteweg-de Vries Equation”, Mod. Phys. Lett. B, 34:25 (2020), 2050270  crossref  mathscinet  isi
    5. Ramirez, J, “New classes of solutions for the Schwarzian Korteweg-de Vries equation in (2+1) dimensions”, Journal of Physics A-Mathematical and Theoretical, 40:16 (2007), 4351  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Ramirez, J, “Multiple solutions for the Schwarzian Korteweg-de Vries equation in (2+1) dimensions”, Chaos Solitons & Fractals, 32:2 (2007), 682  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. M. S. Bruzón, M. L. Gandarias, C. Muriel, J. Ramíres, F. R. Romero, “Traveling-Wave Solutions of the Schwarz–Korteweg–de Vries Equation in $2+1$ Dimensions and the Ablowitz–Kaup–Newell–Segur Equation Through Symmetry Reductions”, Theoret. and Math. Phys., 137:1 (2003), 1378–1389  mathnet  crossref  crossref  mathscinet  isi  elib
    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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