Eur. Phys. J. Plus (2019) 134: 125
https://doi.org/10.1140/epjp/i2019-12541-2

Regular Article

Jacobi elliptic function solutions of the double dispersive equation in the Murnaghan's rod

¹ Department of Information Technology, School of Information Technology and Engineering, Vellore Institute of Technology, Vellore, 632014, Tamilnadu, India
² Department of Mathematics, Faculty of Education, Harran University, Sanliurfa, Turkey
³ Firat University, Faculty of Science, 23119, Elazig, Turkey

^* e-mail: hmbaskonus@gmail.com

Received: 27 October 2018
Accepted: 27 January 2019
Published online: 27 March 2019

Abstract

This research communication aims to obtain the periodic wave solutions of the double dispersive equation of the wave propagation in a nonlinear elastic inhomogeneous Murnaghan's rod by using the F -expansion technique. This method first converts the partial differential equation into an ordinary differential equation under the wave transformation, then the assumed solution converts the problem under study into systems of algebraic equations. Once these algebraic systems are solved for the unknowns and are shifted into the assumed solution, the exact solutions of the double dispersive equation is obtained. Next by making the modulus of Jacobi elliptic functions into either 0 (or) 1, non-topological, singular and their compound solitons are gleaned. The two- and three-dimensional plots are given to show the roving properties of the solutions.