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Novel $(G'/G)$-expansion method; KdV–mKdV equation; travelling wave solutions.

In this article, the novel $(G'/G)$-expansion method is successfully applied to construct the abundant travelling wave solutions to the KdV–mKdV equation with the aid of symbolic computation. This equation is one of the most popular equation in soliton physics and appear in many practical scenarios like thermal pulse, wave propagation of bound particle, etc. The method is reliable and useful, and gives more general exact travelling wave solutions than the existing methods. The solutions obtained are in the form of hyperbolic, trigonometricand rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Many of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed.

SYED TAHIR RAZA RIZVI¹ KASHIF ALI¹ ALI SARDAR² MUHAMMAD YOUNIS³ AHMET BEKIR⁴

1. Department of Mathematics, COMSATS Institute of Information Technology, Lahore, Pakistan
2. Department of Mathematics, National University of Computer and Emerging Sciences, Lahore, Pakistan
3. Centre for Undergraduate Studies, University of Punjab, Lahore 54590, Pakistan
4. Mathematics-Computer Department, Art-Science Faculty, Eskisehir Osmangazi University, 26480, Eskisehir-Turkey

Published

16 January 2017

Manuscript received

5 July 2015

Manuscript revised

21 April 2016

Accepted

6 May 2016

Early published

9 December 2016