A Lie Symmetry Solutions of Sawada-Kotera Equation
DOI:
https://doi.org/10.24297/jam.v17i0.8364Keywords:
Lie SymmetryAbstract
In this article, the Lie Symmetry Analysis is applied in finding the symmetry solutions of the fifth order Sawada-Kotera equation. The technique is among the most powerful approaches currently used to achieveprecise solutions of the partial differential equations that are nonlinear. We systematically show the procedure to obtain the solution which is achieved by developing infinitesimal transformation, prolongations, infinitesimal generatorsand invariant transformations hence symmetry solutions of the fifth order Sawada-Kotera equation.
Key Words- Lie symmetry analysis. Sawada-Kotera equation. Symmetry groups. Prolongations. Invariant solutions. Power series solutions. Symmetry solutions.
Downloads
References
Liu, S., Z. Fu, S. Liu and Q. Zhao. (2001). Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Phys. Lett. A, 289: 69-74
Hirota, R. (1971). Exact solution of the KdV equation for multiple collisions of solutions. Phys. Rev. Lett., 27: 1192-1194.
Rogers, C. and W.F. Shadwick.(1982). Backlund Transformations. Academic Press, New York.
Liao, S.J. (1992). The Homotopy Analysis Methodand its applications in mechanics. Ph.D.Dissertation (In English), Shanghai Jiao TongUniv.
Noor, M.A. and S.T. Mohyud-Din.(2008).Variational iteration method for solving higherordernonlinear boundary value problems usingHe’s polynomials. Int. J. Nonlinear Sci. NumericalSimulation, 9 (2): 141-157.
Oduor, M. O. (2005). Lie symmetry solutions of the generalised Burgers equation. PhD thesis, Maseno university, Kenya.
Khongorzul, D., Hiroyuki, O., & Uuganbayar, Z. (2018). Lie Symmetry Analysis of a class of time fractional nonlinear evolution systems. Elsevier, 1-15.
Dingjiang, H., Xiangxiang, L., & Shunchang, Y. (2017). Lie Symmetry Classification of the Generalised Nonlinear Beam Equation. Symmetry, 9, 1-15.
Aminer, T. (2014). Lie symmetry solution of fourth order nonlinear Ordinary Differential Equation. PhD thesis, Jaramogi Oginga Odinga University of Science and Technology,Kenya.
Andronikos, P., Richard, M., & Peter, G. (2016). Lie Symmetries of (1+2) Nonautonomous Evolution Equations in Financial Mathematics. Mathematics,4, Open Access, 34.
Dingjiang, H., Xiangxiang, L., & Shunchang, Y. (2017). Lie Symmetry Classification of the Generalised Nonlinear Beam Equation. Symmetry, 9, 1-15.
Sakkaravarthi, K., Johnpillai, A., Durga, D., Kanna, T., & Lakshmanan, M. (2018). Lie Symmetry Analysis and Group Invariant Solutions of the nonlinear Helmholtz Equation. arXiv:1803-01622, 1-18.
Yildirim, A. and Z. Pinar.(2010). Application of the exp-function method for solving nonlinear reaction-diffusion equations arising in mathematical biology. Computers and Math. With Applications, 60: 1873-1880
V.A. Galaktionov, S.R. Svirshchevskii. (2006). Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics,Chapman and Hall/CRC.
H. Liu, W. Li.(2008). The exact analytic solutions of a nonlinear differential iterative equation, Nonlinear Anal. 69, 2466–2478.
H. Liu, F. Qiu.(2005). Analytic solutions of an iterative equation with first order derivative, Ann. Differential Equations 21, 337–342.
H. Liu, W. Li.(2006). Discussion on the analytic solutions of the second-order iterative differential equation, Bull. Korean Math. Soc. 43, 791–804.
N.H. Asmar.(2005). Partial Differential Equations with Fourier Series and Boundary Value Problems, second edn., China Machine Press, Beijing.
Downloads
Published
How to Cite
Issue
Section
License
All articles published in Journal of Advances in Linguistics are licensed under a Creative Commons Attribution 4.0 International License.
