Investigation of Exact Solutions of Nonlinear Evolution Equations Using Unified Method

Xiaoming Wang, Shehbaz Ahmad Javed, Abdul Majeed (), Mohsin Kamran and Muhammad Abbas ()
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Xiaoming Wang: School of Mathematics & Computer Science, Shangrao Normal University, Shangrao 334001, China
Shehbaz Ahmad Javed: Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
Abdul Majeed: Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
Mohsin Kamran: Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
Muhammad Abbas: Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan

Mathematics, 2022, vol. 10, issue 16, 1-17

Abstract: In this article, an analytical technique based on unified method is applied to investigate the exact solutions of non-linear homogeneous evolution partial differential equations. These partial differential equations are reduced to ordinary differential equations using different traveling wave transformations, and exact solutions in rational and polynomial forms are obtained. The obtained solutions are presented in the form of 2D and 3D graphics to study the behavior of the analytical solution by setting out the values of suitable parameters. The acquired results reveal that the unified method is a suitable approach for handling non-linear homogeneous evolution equations.

Keywords: exact solutions; unified method (UM); generalized regularized long wave ( GRLW ) equation; modified Zakharov–Kuznetsov equation ( mZK ); traveling wave transformations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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