Bright–Dark Soliton Waves’ Dynamics in Pseudo Spherical Surfaces through the Nonlinear Kaup–Kupershmidt Equation

Mostafa M A Khater,Nawal A Alshehri,Suleman H Alfalqi,Jameel F Alzaidi,Mohammed A El-Shorbagy,Lanre Akinyemi,Sayed K Elagan

doi:10.3390/sym13060963

Mostafa M A Khater, Nawal A Alshehri + Show 5 more

Open Access

https://doi.org/10.3390/sym13060963

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Abstract

The soliton waves’ physical behavior on the pseudo spherical surfaces is studied through the analytical solutions of the nonlinear (1+1)–dimensional Kaup–Kupershmidt (KK) equation. This model is named after Boris Abram Kupershmidt and David J. Kaup. This model has been used in various branches such as fluid dynamics, nonlinear optics, and plasma physics. The model’s computational solutions are obtained by employing two recent analytical methods. Additionally, the solutions’ accuracy is checked by comparing the analytical and approximate solutions. The soliton waves’ characterizations are illustrated by some sketches such as polar, spherical, contour, two, and three-dimensional plots. The paper’s novelty is shown by comparing our obtained solutions with those previously published of the considered model.

Highlights

A significant and prominent portion of the nonlinear partial differential Equation (NLPDE) has recently played a role in describing many physical, chemical, biological, mechanical, optical, and other phenomena in engineering [1,2]. This image aims to identify the new features of each model by finding their moving wave solutions to construct the original and soundscapes for semi-analytical and numerical schemes [3,4,5]
Several mathematicians and physics researchers have focused on the drawing up of accurate analytical, semi–analytical, and numerical schemes such as Khater method, modified Khater method, generalized
The considered model is studied by utilizing some analytical and numerical schemes such as the homotopy perturbation method (HPM) [26], different methods of fixed-point theorem together with the concept of Piccard L-stability [27], the deep geometric theory of Krasil’shchik and Vinogradov that is known with a nonlocal symmetries theory [28], the q-homotopy analysis transform method (q-HATM) [29], the modified auxiliary equation of direct algebraic method [30], the Adomian decomposition method (ADM) [31], perturbation scheme and the Hirota bi-linear formalism [32]

Summary

Introduction

A significant and prominent portion of the nonlinear partial differential Equation (NLPDE) has recently played a role in describing many physical, chemical, biological, mechanical, optical, and other phenomena in engineering [1,2]. This image aims to identify the new features of each model by finding their moving wave solutions to construct the original and soundscapes for semi-analytical and numerical schemes [3,4,5].

Distinct Solutions

NAE Method’s Soliton Solutions

Semi–Analytical Solutions

Results’ Discussion

Conclusions

Methods