Multiple Lump Novel and Accurate Analytical and Numerical Solutions of the Three-Dimensional Potential Yu–Toda–Sasa–Fukuyama Equation

Mostafa M A Khater,Dumitru Baleanu,Mohamed S Mohamed

doi:10.3390/sym12122081

Abstract

The accuracy of novel lump solutions of the potential form of the three–dimensional potential Yu–Toda–Sasa–Fukuyama (3-Dp-YTSF) equation is investigated. These solutions are obtained by employing the extended simplest equation (ESE) and modified Kudryashov (MKud) schemes to explore its lump and breather wave solutions that characterizes the dynamics of solitons and nonlinear waves in weakly dispersive media, plasma physics, and fluid dynamics. The accuracy of the obtained analytical solutions is investigated through the perspective of numerical and semi-analytical strategies (septic B-spline (SBS) and variational iteration (VI) techniques). Additionally, matching the analytical and numerical solutions is represented along with some distinct types of sketches. The superiority of the MKud is showed as the fourth research paper in our series that has been beginning by Mostafa M. A. Khater and Carlo Cattani with the title “Accuracy of computational schemes”. The functioning of employed schemes appears their effectual and ability to apply to different nonlinear evolution equations.

Highlights

Soliton is one of the most well-known properties that characterize the integrability of nonlinear evolution equations [1,2]
A new branch of the rogue wave is known as a lump wave which is defined by a restricted rogue wave in every direction in space [10,11,12]
This calculating shows the arrogance of the modified Kudryashov (MKud) method over the extended simplest equation (ESE) method where its absolute values of error are much smaller than that have been obtained by the ESE method (Figure 6)

Summary

Introduction

Soliton is one of the most well-known properties that characterize the integrability of nonlinear evolution equations [1,2]. The rogue waves or monster waves, freak waves, abnormal waves have been observed as one of the soliton waves which are an exceptional type of nonlinear waves that are restricted in just one direction and have much significance in a variety of physical branches [3,4]. These waves are first figured out in the deep ocean [5,6].

Analytical and Numerical Matching for the 3-Dp-YTSF Equation

Conclusions