Eur. Phys. J. Plus (2021) 136: 455
https://doi.org/10.1140/epjp/s13360-021-01472-2

Regular Article

Closed-form solutions to the new coupled Konno–Oono equation and the Kaup–Newell model equation in magnetic field with novel statistic application

¹ Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
² Department of Mathematics, Faculty of Science, Mansoura University, 35516, Mansoura, Egypt
³ Department of Mathematics, Faculty of Science, Damietta University, 34517, New Damietta, Egypt

^a mahmoud.abdelrahman@mans.edu.eg, maabdelrahman@taibahu.edu.sa

Received: 28 July 2020
Accepted: 21 April 2021
Published online: 27 April 2021

Abstract

This paper employs the new robust solver to retrieve exact solutions to a Kaup–Newell model equation and the nonlinear coupled Konno–Oono equation. This solver yields the closed formula for the solutions. Different types of travelling wave solutions, i.e., rational function, hyperbolic function and trigonometric function solutions with many capricious parameters are revealed. Subsequently, by utilizing Matlab 18 we plot 2D and 3D surfaces of obtained analytical solutions for suitable values of the free parameters. The depiction of the solver is direct, vital, sturdy and can be applied to other nonlinear partial differential equations. We also show that some proposed rational solutions can be rapprochement with some known probability distributions.