Abundant closed-form solutions and solitonic structures to an integrable fifth-order generalized nonlinear evolution equation in plasma physics
This paper investigates the evolution dynamics of closed-form solutions for a new integrable nonlinear fifth-order equation with spatial and temporal dispersion which describes shallow water waves moving in two directions. Some novel computational soliton solutions are obtained in the form of expone...
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doaj-543870400d5849b7879eb914555b9ce52021-06-27T04:37:24ZengElsevierResults in Physics2211-37972021-07-0126104453Abundant closed-form solutions and solitonic structures to an integrable fifth-order generalized nonlinear evolution equation in plasma physicsSachin Kumar0Hassan Almusawa1Ihsanullah Hamid2M.A. Abdou3Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi-110007, India; Corresponding author.Department of Mathematics, College of Sciences, Jazan University, Jazan 45142, Saudi ArabiaDepartment of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi-110007, IndiaDepartment of Mathematics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia; Physics Department, Faculty of Science, Mansoura University, Mansoura 35516, EgyptThis paper investigates the evolution dynamics of closed-form solutions for a new integrable nonlinear fifth-order equation with spatial and temporal dispersion which describes shallow water waves moving in two directions. Some novel computational soliton solutions are obtained in the form of exponential rational functions, trigonometric and hyperbolic functions, and complex-soliton solutions. Some dynamical wave structures of soliton solutions are achieved in evolutionary dynamical structures of multi-wave solitons, double-solitons, triple-solitons, multiple solitons, breather-type solitons, Lump-type solitons, singular solitons, and Kink-wave solitons using the generalized exponential rational function (GERF) technique. All newly established solutions are verified by back substituting into the considered fifth-order nonlinear evolution equation using computerized symbolic computational work via Wolfram Mathematica. These newly formed results demonstrate that the considered fifth-order equation theoretically possesses very rich computational wave structures of closed-form solutions, which are also useful in obtaining a better understanding of the internal mechanism of other complex nonlinear physical models arising in the field of plasma physics and nonlinear sciences. The physical characteristics of some constructed solutions are also graphically displayed via three-dimensional plots by selecting the best appropriate constant parameter values to easily understand the complex physical phenomena of the nonlinear equations. Eventually, the results validate the effectiveness and trustworthiness of the used technique.http://www.sciencedirect.com/science/article/pii/S2211379721005684Fifth-order nonlinear evolution equationDynamical structuresGERF methodClosed-form solutionsSolitons |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Sachin Kumar Hassan Almusawa Ihsanullah Hamid M.A. Abdou |
spellingShingle |
Sachin Kumar Hassan Almusawa Ihsanullah Hamid M.A. Abdou Abundant closed-form solutions and solitonic structures to an integrable fifth-order generalized nonlinear evolution equation in plasma physics Results in Physics Fifth-order nonlinear evolution equation Dynamical structures GERF method Closed-form solutions Solitons |
author_facet |
Sachin Kumar Hassan Almusawa Ihsanullah Hamid M.A. Abdou |
author_sort |
Sachin Kumar |
title |
Abundant closed-form solutions and solitonic structures to an integrable fifth-order generalized nonlinear evolution equation in plasma physics |
title_short |
Abundant closed-form solutions and solitonic structures to an integrable fifth-order generalized nonlinear evolution equation in plasma physics |
title_full |
Abundant closed-form solutions and solitonic structures to an integrable fifth-order generalized nonlinear evolution equation in plasma physics |
title_fullStr |
Abundant closed-form solutions and solitonic structures to an integrable fifth-order generalized nonlinear evolution equation in plasma physics |
title_full_unstemmed |
Abundant closed-form solutions and solitonic structures to an integrable fifth-order generalized nonlinear evolution equation in plasma physics |
title_sort |
abundant closed-form solutions and solitonic structures to an integrable fifth-order generalized nonlinear evolution equation in plasma physics |
publisher |
Elsevier |
series |
Results in Physics |
issn |
2211-3797 |
publishDate |
2021-07-01 |
description |
This paper investigates the evolution dynamics of closed-form solutions for a new integrable nonlinear fifth-order equation with spatial and temporal dispersion which describes shallow water waves moving in two directions. Some novel computational soliton solutions are obtained in the form of exponential rational functions, trigonometric and hyperbolic functions, and complex-soliton solutions. Some dynamical wave structures of soliton solutions are achieved in evolutionary dynamical structures of multi-wave solitons, double-solitons, triple-solitons, multiple solitons, breather-type solitons, Lump-type solitons, singular solitons, and Kink-wave solitons using the generalized exponential rational function (GERF) technique. All newly established solutions are verified by back substituting into the considered fifth-order nonlinear evolution equation using computerized symbolic computational work via Wolfram Mathematica. These newly formed results demonstrate that the considered fifth-order equation theoretically possesses very rich computational wave structures of closed-form solutions, which are also useful in obtaining a better understanding of the internal mechanism of other complex nonlinear physical models arising in the field of plasma physics and nonlinear sciences. The physical characteristics of some constructed solutions are also graphically displayed via three-dimensional plots by selecting the best appropriate constant parameter values to easily understand the complex physical phenomena of the nonlinear equations. Eventually, the results validate the effectiveness and trustworthiness of the used technique. |
topic |
Fifth-order nonlinear evolution equation Dynamical structures GERF method Closed-form solutions Solitons |
url |
http://www.sciencedirect.com/science/article/pii/S2211379721005684 |
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