10.30495/ijm2c.2023.1974373.1269

Examining (3+1)- ‎Dimensional Extended Sakovich Equation Using Lie Group Methods

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  • Yadollah AryaNejad*1,
  • Mehdi Jafari2,
  • Asma Khalili3,
  1. Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, I.R. of Iran
  2. ‎Department of Mathematics, Payame Noor University, P‎.O. ‎Box‎ 19395-3697, Tehran, I.R. ‎of Iran.
  3. Payame Noor University

Received: 01-02-2023

Accepted: 15-03-2023

Published in Issue 01-06-2023

Copyright (c) 2024 International Journal of Mathematical Modeling & Computations

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

AryaNejad, Y., Jafari, M., & Khalili, A. (2023). Examining (3+1)- ‎Dimensional Extended Sakovich Equation Using Lie Group Methods. International Journal of Mathematical Modelling & Computations, 13(2), 0-0. https://doi.org/10.30495/ijm2c.2023.1974373.1269
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Abstract

In this paper, we investigate the symmetry group of the (3 + 1)-dimensional Sakovich equation. We obtain the classical and non-classical Lie symmetries for the equation under consideration. Therefore, we respond to the question of classification of the equation symmetries and, as a result, its invariant solutions. Presenting the algebra of symmetries and utilizing Ibragimov’s method, we create the optimal system of Lie subalgebras. We obtain the symmetry reductions and invariant solutions of the considered equation using these vector fields.

Keywords

  • Lie algebras,
  • r‎eduction equations,
  • ‎ Extended Sakovich equation‎,
  • Invariant s‎olution‎
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References

  1. S. C. Anco, M. L. Gandarias and E. Recio, Line-solitons, line-shocks, and conservation laws of a
  2. universal KP-like equation in 2+1 dimensions, J. Math. Anal. Appl., 504 (2021) 125319.
  3. Y. AryaNejad, Exact solutions of diffusion equation on sphere, Comput. Methods Differ. Equ., 10
  4. (3) (2022) 789–798.
  5. Y. AryaNejad, Symmetry Analysis of Wave Equation on Conformally Flat Spaces, J. Geom. Phys.,
  6. (2021) 104029.
  7. Y. AryaNejad, R. Mirzavand, Conservation laws and invariant solutions of time-dependent CalogeroBogoyavlenskii-Schiff equation, J. Linear. Topological. Algebra., 11 (4) (2022) 243–252.
  8. G. W. Bluman and S. C. Anco, Symmetry and Integration Methods for Differential Equations,
  9. Springer, (2002).
  10. M. S. Bruzon, M. l. Gandarias, C. Muriel, J. Ramierez, G. S. Saez and F. R.Romero, The CalogeroBogoyavlenskii-Schiff equation in (z+1) dimensions, Theor. Math. phys., 137 (1) (2003) 1367–1377.
  11. G. Cai, Y. Wang and F. Zhang, Nonclassical symmetries and group invariant solutions of BurgersFisher equations, World Journal of Modelling and Simulation, 3 (4) (2007) 305–309.
  12. E. Dastranj and H. Sahebi Fard, Exact solutions and numerical simulation for Bakstein-Howison
  13. model, Computational Methods for Differential Equations, 10 (2) (2022) 461–474.
  14. M. L. Gandarias, M. Torrisi and A. Valenti, Symmetry classification, and optimal systems of a
  15. non-linear wave equation Internet, J. Non-linear Mech., 39 (2004) 389–398.
  16. N. H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, New Trends in
  17. Theoretical Developments and Computational Methods, CRC Press, Boca Raton, Vol. 3, (1996).
  18. M. Jafari, A. Zaeim and A. Tanhaeivash, Symmetry group analysis and conservation laws of the
  19. potential modified KdV equation using the scaling method, Int. J. Geometric Methods in Modern,
  20. (7) (2022) 2250098.
  21. A. P. Mrquez, T. M. Garrido, E. Recio and R. de la Rosa, Lie symmetries and exact solutions for a
  22. fourth-order nonlinear diffusion equation, Math. Meth. Appl. Sci., 45 (17) (2022) 10614–10627.
  23. P. J. Olver, Applications of Lie Groups to Differential Equations, Springer, New York, (1986).
  24. L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, (1982).
  25. Y. S. Ozkan and E. Yasar, Multiwave and interaction solutions and Lie symmetry analysis to a new
  26. (2 + 1)-dimensional Sakovich equation, Alexandria Engineering Journal, 59 (6) (2020) 5285–5293.
  27. S. Rashidi and S. R. Hejazi, Self-adjointness, conservation laws and invariant solutions of the Buckmaster equation, Computational Methods for Differential Equations, 8 (1) (2020) 85–98.
  28. S. Sakovich, A new Painlev-integrable equation possessing KdV-type solitons, Nonlinear Phenomena
  29. in Complex Systems, 22 (3) (2019) 299–304.
  30. A. M. Wazwaz, New Painleve-integrable (2+ 1) and (3+ 1)- dimensional KdV and mKdV equations,
  31. Rom. J. Phys., 65 (2020) 108.
  32. A. M. Wazwaz, Two new Painlev-integrabl extended Sakovich equations with (2 + 1) and (3 + 1)
  33. dimensions, International Journal of Numerical Methods for Heat and Fluid Flow, 30 (3) (2020)

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