Soliton solution with different assumptions through Modified Korteweg-de Vries (MKDV) Equation: Exact analytical solution

Sami Alghamdi, Muhammad Asad Iqbal, Muzamal Hussain, Muhammad Taj, Mohamed Amien Khadimallah, Elimam Ali and Abdur Rauf

Abstract

In the present work, nonlinear partial differential equations in its original form are used to obtain soliton solutions for the problem. The equations considered are of practical use since most of them have many applications in our daily life. In particular, the soliton solutions of nonlinear partial differential equations are obtained using a modified version of the expfunction method. Mathematical code for modified exp-function method is developed by making use of the software named MAPLE. Three solutions as assumption-I, assumption-II and assumption-III are utilized with modified form of exp-function method equation. In order to interpret obtained soliton solutions into meaningful form, aid of graphical simulations would be taken using computer softwares MATHEMATICA and MATLAB.

Key Words

assumptions; code; equations; exp-function method; MATHEMATICA and MATLAB; soliton solutions

Address

(1) Sami Alghamdi: Electrical and Computer Engineering Department, King Abdulaziz University, Jeddah, Saudi Arabia; (2) Muhammad Asad Iqbal: Department of Mathematics, University of Poonch Rawalakot, AJK, Pakistan; (3) Muzamal Hussain: Department of Mathematics, University of Sahiwal, 57000, Sahiwal, Pakistan; (4) Muhammad Taj: Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan; (5) Mohamed Amien Khadimallah, Elimam Ali: Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia; (6) Abdur Rauf: Department of Chemistry, University of Sahiwal, 57000, Sahiwal, Pakistan.

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