(6)Modified ( G' / G )-expansion method for finding traveling wave solutions of the coupled Benjamin–Bona–Mahony-KdV equation

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Vikas Kumar

Department of Mathematics, D.A.V. College Pundri, Kaithal 136026, Haryana, India 

Received 28 March 2019; received in revised form 25 April 2019; accepted 26 April 2019 

Available online 7 May 2019 

Abstract  

Using the Lie symmetry approach, the author has examined traveling wave solutions of coupled Benjamin–Bona–Mahony-KdV equation. The coupled Benjamin–Bona–Mahony-KdV equation is reduced to nonlinear ordinary differential equations for all optimal subalgebras by using Lie classical symmetries and various solutions are obtained by the modified ( G'/ G )-expansion method. Further, with the aid of solutions of the nonlinear ordinary differential equations, more explicit traveling wave solutions of the coupled Benjamin–Bona–Mahony-KdV equation are found out. The traveling wave solutions are expressed by rational function. 

© 2019 Shanghai Jiaotong University. Published by Elsevier B.V. 

This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)  

Keywords: Coupled Benjamin–Bona–Mahony-KdV equation; Lie symmetric analysis; Exact solutions; Modified ( G'/ G )-Expansion method.