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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)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

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

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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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