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Symmetry 2018, 10(8), 341; https://doi.org/10.3390/sym10080341

Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Sixth-Order Nonlinear Ramani Equation

1
Department of Mathematics, Science Faculty, Firat University, Elazig 23119, Turkey
2
Department of Mathematics, Faculty of Science, Federal University Dutse, Dutse 71560, Nigeria
3
Department of Mathematics, Cankaya University, Ankara 06790, Turkey
4
Institute of Space Sciences, Magurele 077126, Romania
*
Author to whom correspondence should be addressed.
Received: 11 July 2018 / Revised: 8 August 2018 / Accepted: 9 August 2018 / Published: 15 August 2018
(This article belongs to the Special Issue Symmetry of Lie Algebras)
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Abstract

In this work, we study the completely integrable sixth-order nonlinear Ramani equation. By applying the Lie symmetry analysis technique, the Lie point symmetries and the optimal system of one-dimensional sub-algebras of the equation are derived. The optimal system is further used to derive the symmetry reductions and exact solutions. In conjunction with the Riccati Bernoulli sub-ODE (RBSO), we construct the travelling wave solutions of the equation by solving the ordinary differential equations (ODEs) obtained from the symmetry reduction. We show that the equation is nonlinearly self-adjoint and construct the conservation laws (CL) associated with the Lie symmetries by invoking the conservation theorem due to Ibragimov. Some figures are shown to show the physical interpretations of the acquired results. View Full-Text
Keywords: Lie symmetry analysis; conservation laws; traveling wave solutions Lie symmetry analysis; conservation laws; traveling wave solutions
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Aliyu, A.I.; Inc, M.; Yusuf, A.; Baleanu, D. Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Sixth-Order Nonlinear Ramani Equation. Symmetry 2018, 10, 341.

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