Travelling waves solutions for modified Korteweg-de Vries equation by modified Exp-function method

Muhammad Asad Iqbal , Muzamal Hussain , Muhammad Safeer , Muhammad Taj , Abdelouahed Tounsi

Abstract

Nonlinearity occurs in abundance in nature and most of these nonlinear phenomena's are of great importance. Many of these nonlinear phenomena's can be modeled in the form of nonlinear partial differential equations. Among nonlinear partial differential equations an important class is that of evolution equations. Evolution equations arise in many areas such as modeling of water waves. In this work, a modified version of Exp-function method is used to find analytical solutions of Modified KdV equation. The results obtained are verified by substituting them back into the original differential equations. Moreover, to re-verify the results, 2 dimensional and 3 dimensional plots for each of the solution sets are also plotted.

Key Words

Exp-function; modified KdV equation; nonlinear phenomena; partial differential equations

Address

Muhammad Asad Iqbal — Department of Mathematics, University of Poonch, Rawalakot, AJK, Pakistan
Muzamal Hussain — Department of Mathematics, University of Sahiwal, Sahiwal, 57000, Faisalabad, Pakistan
Muhammad Safeer and Muhammad Taj — Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan
Abdelouahed Tounsi — 1) YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea, 2) Department of Civil and Environmental Engineering, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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