Dynamical behaviour of travelling wave solutions to the conformable time-fractional modified Liouville and mRLW equations in water wave mechanics
In this current study, we described a modified extended tanh-function (mETF) method to find the new and efficient exact travelling and solitary wave solutions to the modified Liouville equation and modified regularized long wave (mRLW) equation in water wave mechanics. Travelling wave transformation...
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| Format: | Article |
| Language: | English |
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Elsevier
2021-08-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844021018077 |
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| author | Abdulla - Al Mamun Samsun Nahar Ananna Tianqing An Nur Hasan Mahmud Shahen Md. Asaduzzaman Foyjonnesa |
| author_facet | Abdulla - Al Mamun Samsun Nahar Ananna Tianqing An Nur Hasan Mahmud Shahen Md. Asaduzzaman Foyjonnesa |
| author_sort | Abdulla - Al Mamun |
| collection | DOAJ |
| description | In this current study, we described a modified extended tanh-function (mETF) method to find the new and efficient exact travelling and solitary wave solutions to the modified Liouville equation and modified regularized long wave (mRLW) equation in water wave mechanics. Travelling wave transformation decreases the leading equation to traditional ordinary differential equations (ODEs). The standardized balance technique provides the instruction of the portended polynomial related result stimulated from the mETF method. The substitution of this result follows the preceding step. Balancing the coefficients of the like powers of the portended solution leads to a system of algebraic equations (SAE). The solution of that SAE for coefficients provides the essential connection between the coefficients and the parameters to build the exact solution. Here the acquired solutions are hyperbolic, rational, and trigonometric function solutions. Our mentioned method is straightforward, succinct, efficient, and powerful and can be emphasized to establish the new exact solutions of different types of nonlinear conformable fractional equations in engineering and further nonlinear treatments. |
| first_indexed | 2024-12-21T21:54:47Z |
| format | Article |
| id | doaj.art-c471a2bbfd9448a583e1a34d9d897a5b |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-12-21T21:54:47Z |
| publishDate | 2021-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-c471a2bbfd9448a583e1a34d9d897a5b2022-12-21T18:49:00ZengElsevierHeliyon2405-84402021-08-0178e07704Dynamical behaviour of travelling wave solutions to the conformable time-fractional modified Liouville and mRLW equations in water wave mechanicsAbdulla - Al Mamun0Samsun Nahar Ananna1Tianqing An2Nur Hasan Mahmud Shahen3Md. Asaduzzaman4 Foyjonnesa5Department of Mathematics, College of Science, Hohai University, Nanjing-210098, PR China; School of Science and Engineering, AM's Research Academy, Dhaka, Bangladesh; Department of Mathematics, Islamic University, Kushtia-7003, Bangladesh; Corresponding author at: Department of Mathematics, College of Science, Hohai University, Nanjing-210098, PR China.Department of Mathematics, College of Science, Hohai University, Nanjing-210098, PR China; School of Science and Engineering, AM's Research Academy, Dhaka, Bangladesh; Department of Mathematics, Islamic University, Kushtia-7003, BangladeshDepartment of Mathematics, College of Science, Hohai University, Nanjing-210098, PR ChinaDepartment of Arts and Sciences, Bangladesh Army University of Science and Technology, Saidpur-5310, Bangladesh; Department of Mathematics, European University of Bangladesh, Dhaka-1216, BangladeshDepartment of Mathematics, Islamic University, Kushtia-7003, BangladeshDepartment of Mathematics, European University of Bangladesh, Dhaka-1216, BangladeshIn this current study, we described a modified extended tanh-function (mETF) method to find the new and efficient exact travelling and solitary wave solutions to the modified Liouville equation and modified regularized long wave (mRLW) equation in water wave mechanics. Travelling wave transformation decreases the leading equation to traditional ordinary differential equations (ODEs). The standardized balance technique provides the instruction of the portended polynomial related result stimulated from the mETF method. The substitution of this result follows the preceding step. Balancing the coefficients of the like powers of the portended solution leads to a system of algebraic equations (SAE). The solution of that SAE for coefficients provides the essential connection between the coefficients and the parameters to build the exact solution. Here the acquired solutions are hyperbolic, rational, and trigonometric function solutions. Our mentioned method is straightforward, succinct, efficient, and powerful and can be emphasized to establish the new exact solutions of different types of nonlinear conformable fractional equations in engineering and further nonlinear treatments.http://www.sciencedirect.com/science/article/pii/S2405844021018077Modified extended tanh-function methodModified Liouville equationModified regularized long-wave equationExact solutionTravelling wave solution |
| spellingShingle | Abdulla - Al Mamun Samsun Nahar Ananna Tianqing An Nur Hasan Mahmud Shahen Md. Asaduzzaman Foyjonnesa Dynamical behaviour of travelling wave solutions to the conformable time-fractional modified Liouville and mRLW equations in water wave mechanics Heliyon Modified extended tanh-function method Modified Liouville equation Modified regularized long-wave equation Exact solution Travelling wave solution |
| title | Dynamical behaviour of travelling wave solutions to the conformable time-fractional modified Liouville and mRLW equations in water wave mechanics |
| title_full | Dynamical behaviour of travelling wave solutions to the conformable time-fractional modified Liouville and mRLW equations in water wave mechanics |
| title_fullStr | Dynamical behaviour of travelling wave solutions to the conformable time-fractional modified Liouville and mRLW equations in water wave mechanics |
| title_full_unstemmed | Dynamical behaviour of travelling wave solutions to the conformable time-fractional modified Liouville and mRLW equations in water wave mechanics |
| title_short | Dynamical behaviour of travelling wave solutions to the conformable time-fractional modified Liouville and mRLW equations in water wave mechanics |
| title_sort | dynamical behaviour of travelling wave solutions to the conformable time fractional modified liouville and mrlw equations in water wave mechanics |
| topic | Modified extended tanh-function method Modified Liouville equation Modified regularized long-wave equation Exact solution Travelling wave solution |
| url | http://www.sciencedirect.com/science/article/pii/S2405844021018077 |
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