A reduction technique to solve the generalized nonlinear dispersive mK(m,n) equation with new local derivative
In this work, we consider the generalized nonlinear dispersive mK(m,n) equation with a recently defined local derivative in the temporal direction. Different types of exact solutions are extracted by Nucci’s reduction technique. Combinations of the exponential, trigonometric, hyperbolic, and logarit...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-07-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379722002534 |
| _version_ | 1818470635914919936 |
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| author | Fang-Li Xia Fahd Jarad Mir Sajjad Hashemi Muhammad Bilal Riaz |
| author_facet | Fang-Li Xia Fahd Jarad Mir Sajjad Hashemi Muhammad Bilal Riaz |
| author_sort | Fang-Li Xia |
| collection | DOAJ |
| description | In this work, we consider the generalized nonlinear dispersive mK(m,n) equation with a recently defined local derivative in the temporal direction. Different types of exact solutions are extracted by Nucci’s reduction technique. Combinations of the exponential, trigonometric, hyperbolic, and logarithmic functions constitute the exact solutions especially of the soliton and Kink-type soliton solutions. The influence of the derivative order α, for the obtained results, is graphically investigated. In some cases, exact solutions are achieved for arbitrary values of n and m, which can be interesting from the mathematical point of view. We provided 2-D and 3-D figures to illustrate the reported solutions. Computational results indicate that the reduction technique is superior to some other methods used in the literature to solve the same equations. To the best of the author’s knowledge, this method is not applied for differential equations with the recently hyperbolic local derivative. |
| first_indexed | 2024-04-13T21:39:39Z |
| format | Article |
| id | doaj.art-32922de3f1c94c8b947ae3ad7a79143e |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-13T21:39:39Z |
| publishDate | 2022-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-32922de3f1c94c8b947ae3ad7a79143e2022-12-22T02:28:48ZengElsevierResults in Physics2211-37972022-07-0138105512A reduction technique to solve the generalized nonlinear dispersive mK(m,n) equation with new local derivativeFang-Li Xia0Fahd Jarad1Mir Sajjad Hashemi2Muhammad Bilal Riaz3College of Science, Hunan City University, Yiyang 413000, PR ChinaDepartment of Mathematics, Çankaya University, Etimesgut 06790, Ankara, Turkey; Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia; Department of Medical Research, China Medical University, Taichung 40402, Taiwan; Corresponding author.Department of Mathematics, Basic Science Faculty, University of Bonab, P.O. Box 55513-95133, Bonab, IranDepartment of Mathematics, University of Management and Technology Lahore, 54770 Pakistan; Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924 Lodz, Poland; Institute for Groundwater Studies, University of the Free State, 9301, Bloemfontein, South Africa; Corresponding author at: Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924 Lodz, Poland.In this work, we consider the generalized nonlinear dispersive mK(m,n) equation with a recently defined local derivative in the temporal direction. Different types of exact solutions are extracted by Nucci’s reduction technique. Combinations of the exponential, trigonometric, hyperbolic, and logarithmic functions constitute the exact solutions especially of the soliton and Kink-type soliton solutions. The influence of the derivative order α, for the obtained results, is graphically investigated. In some cases, exact solutions are achieved for arbitrary values of n and m, which can be interesting from the mathematical point of view. We provided 2-D and 3-D figures to illustrate the reported solutions. Computational results indicate that the reduction technique is superior to some other methods used in the literature to solve the same equations. To the best of the author’s knowledge, this method is not applied for differential equations with the recently hyperbolic local derivative.http://www.sciencedirect.com/science/article/pii/S2211379722002534Nucci’s reduction methodLocal derivativeGeneralized nonlinear dispersive mK(m,n) equation |
| spellingShingle | Fang-Li Xia Fahd Jarad Mir Sajjad Hashemi Muhammad Bilal Riaz A reduction technique to solve the generalized nonlinear dispersive mK(m,n) equation with new local derivative Results in Physics Nucci’s reduction method Local derivative Generalized nonlinear dispersive mK(m,n) equation |
| title | A reduction technique to solve the generalized nonlinear dispersive mK(m,n) equation with new local derivative |
| title_full | A reduction technique to solve the generalized nonlinear dispersive mK(m,n) equation with new local derivative |
| title_fullStr | A reduction technique to solve the generalized nonlinear dispersive mK(m,n) equation with new local derivative |
| title_full_unstemmed | A reduction technique to solve the generalized nonlinear dispersive mK(m,n) equation with new local derivative |
| title_short | A reduction technique to solve the generalized nonlinear dispersive mK(m,n) equation with new local derivative |
| title_sort | reduction technique to solve the generalized nonlinear dispersive mk m n equation with new local derivative |
| topic | Nucci’s reduction method Local derivative Generalized nonlinear dispersive mK(m,n) equation |
| url | http://www.sciencedirect.com/science/article/pii/S2211379722002534 |
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