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Research Article

Similarity solutions and conservation laws for the Bogoyavlensky-Konopelchenko equation by Lie point symmetries

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Pages 815-827 | Received 19 Jan 2019, Published online: 13 Jul 2020

References

  • M.A. Abdulwahhab, Comment on the paper on conservation laws by Lie symmetry analysis for (2+1)-dimensional Bogoyavlensky-Konopelchenko equation in wave propagation by S. Saha Ray, Computers & Mathematics with Applications 75(12) (2018), 4300–4304. doi: 10.1016/j.camwa.2018.03.030
  • S.C. Anco and G. Bluman, Direct construction method for conservation laws of partial differential equations Part I: Examples of conservation law classifications, European Journal of Applied Mathematics 13(5) (2002), 545–566. doi: 10.1017/S095679250100465X
  • S.C. Anco and G. Bluman, Direct construction method for conservation laws of partial differential equations Part II: General treatment, European Journal of Applied Mathematics 13(5) (2002), 567–585. doi: 10.1017/S0956792501004661
  • L.Y. Bahar and H.G. Kwatny, Extension of Noether’s theorem to constrained non-conservative dynamical systems, International journal of non-linear mechanics 22(2) (1987), 125–138. doi: 10.1016/0020-7462(87)90015-1
  • O.I. Bogoyavlenskii, Overturning solitons in new two-dimensional integrable equations, Izvestiya: Mathematics 34(2) (1990), 245–259. doi: 10.1070/IM1990v034n02ABEH000628
  • F. Calogero, A method to generate solvable nonlinear evolution equations, Lettere al Nuovo Cimento 14(12) (1975), 443–447. doi: 10.1007/BF02763113
  • S. Dimas, Partial differential equations, algebraic computing and nonlinear systems, Ph.D. Thesis, University of Patras, Greece, 2008.
  • S. Dimas and D. Tsoubelis, SYM: A new symmetry-finding package for Mathematica, In: Proceedings of the 10th International Conference in Modern Group Analysis, pp. 64–70, University of Cyprus, Cyprus, October 2004.
  • S. Dimas and D. Tsoubelis, A new Mathematica-based program for solving overdetermined systems of PDEs, In: 8th International Mathematica Symposium, Avignon June 2006, Available at: http://www.internationalmathematicasymposium.org/IMS2006/IMS2006 CD/articles/Dimas.pdf
  • H.C. Hu, New positon, negaton and complexiton solutions for the Bogoyavlensky-Konoplechenko equation, Physics Letters A 373(20) (2009), 1750–1753. doi: 10.1016/j.physleta.2009.03.022
  • N.H. Ibragimov, Nonlinear self-adjointness and conservation laws, Journal of Physics A: Mathematical and Theoretical 44(43) (2011), 432002. doi: 10.1088/1751-8113/44/43/432002
  • N.H. Ibragimov, A new conservation theorem, Journal of Mathematical Analysis and Applications 333(1) (2007), 311–328. doi: 10.1016/j.jmaa.2006.10.078
  • N. Kallinikos and E. Meletidou, Symmetries of charged particle motion under time-independent electromagnetic fields, Journal of Physics A: Mathematical and Theoretical 46(30) (2013), 305202. doi: 10.1088/1751-8113/46/30/305202
  • B.G. Konopelchenko, Solitons in multidimensions: inverse spectral transform method, World Scientific Publishing Co. Pte. Ltd., Singapore, 1993.
  • B.G. Konopelchenko and V.G. Dubrovsky, Some new integrable nonlinear evolution equations in (2+1)-dimensions, Physics Letters A 102(1–2) (1984), 15–17. doi: 10.1016/0375-9601(84)90442-0
  • M.V. Prabhakar and H. Bhate, Exact solutions of the Bogoyavlensky-Konoplechenko equation, Letters in Mathematical Physics 64(1) (2003), 1–6. doi: 10.1023/A:1024909327151
  • S.S. Ray, On conservation laws by Lie symmetry analysis for (2+1)-dimensional Bogoyavlensky-Konopelchenko equation in wave propagation, Computers & Mathematics with Applications 74(6) (2017), 1158–1165. doi: 10.1016/j.camwa.2017.06.007
  • S.S. Ray, Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky-Konopelchenko equation by geometric approach, Modern Physics Letters B 32(11) (2018), 1850127. doi: 10.1142/S0217984918501270
  • K. Toda and S.J. Yu, A study of the construction of equations in (2+1) dimensions, Inverse Problems 17(4) (2001), 1053. doi: 10.1088/0266-5611/17/4/331
  • R. Traciná, M.S. Bruzón, M.L. Gandarias, and M. Torrisi, Nonlinear self-adjointness, conservation laws, exact solutions of a system of dispersive evolution equations, Communications in Nonlinear Science and Numerical Simulation 19(9) (2014), 3036–3043. doi: 10.1016/j.cnsns.2013.12.005
  • H. Triki, Z. Jovanoski, and A. Biswas, Shock wave solutions to the Bogoyavlensky-Konopelchenko equation, Indian Journal of Physics 88(1) (2014), 71–74. doi: 10.1007/s12648-013-0380-7

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