ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

A Novel Scheme for Nonlinear Evolution Equations Using Symbolic Computations

Journal of Applied Nonlinear Dynamics 8(3) (2019) 463--473 | DOI:10.5890/JAND.2019.09.009

Yakup Yıldırım$^{1}$, Elif Yaşar$^{1}$, Abdullahi Rashid Adem$^{2}$, Emrullah Yaşar$^{1}$

$^{1}$ Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059 Gorukle, Bursa, Turkey

$^{2}$ Material Science Innovation and Modelling Focus Area, School of Mathematical and Statistical Sciences, North-West University, Private Bag X 2046, Mmabatho 2735, South Africa

Abstract

In this study a novel method, namely multiple exponential function scheme is performed for nonlinear evolution equations. Based on ﬁrst order auxiliary equations, one-, two-, and three-wave solutions can be established by using computerized symbolic computations. For illustrating the eﬀectiveness of this approach, we apply the method to solve (3+1) dimensional classical Jimbo-Miwa and it’s extended (3+1) dimensional forms. In addition, we determine dispersion relation and phase shift for each of the models.

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