Competent closed form soliton solutions to the Riemann wave equation and the Novikov-Veselov equation
The Riemann wave equation and the Novikov-Veselov equation are interesting nonlinear equations in the sphere of tidal and tsunami waves in ocean, river, ion and magneto-sound waves in plasmas, electromagnetic waves in transmission lines, homogeneous and stationary media etc. In this article, the gen...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-06-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379720305301 |
| _version_ | 1818932689318707200 |
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| author | Hemonta Kumar Barman Aly R. Seadawy M. Ali Akbar Dumitru Baleanu |
| author_facet | Hemonta Kumar Barman Aly R. Seadawy M. Ali Akbar Dumitru Baleanu |
| author_sort | Hemonta Kumar Barman |
| collection | DOAJ |
| description | The Riemann wave equation and the Novikov-Veselov equation are interesting nonlinear equations in the sphere of tidal and tsunami waves in ocean, river, ion and magneto-sound waves in plasmas, electromagnetic waves in transmission lines, homogeneous and stationary media etc. In this article, the generalized Kudryashov method is executed to demonstrate the applicability and effectiveness to extract travelling and solitary wave solutions of higher order nonlinear evolution equations (NLEEs) via the earlier stated equations. The technique is enucleated to extract solitary wave solutions in terms of trigonometric, hyperbolic and exponential function. We acquire bell shape soliton, consolidated bell shape soliton, compacton, singular kink soliton, flat kink shape soliton, smooth singular soliton and other types of soliton solutions by setting particular values of the embodied parameters. For the precision of the result, the solutions are graphically illustrated in 3D and 2D. The analytic solutions greatly facilitate the verification of numerical solvers on the stability analysis of the solution. |
| first_indexed | 2024-12-20T04:36:29Z |
| format | Article |
| id | doaj.art-6f771af9603e44a9816ae88b5c38c3de |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-20T04:36:29Z |
| publishDate | 2020-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-6f771af9603e44a9816ae88b5c38c3de2022-12-21T19:53:15ZengElsevierResults in Physics2211-37972020-06-0117103131Competent closed form soliton solutions to the Riemann wave equation and the Novikov-Veselov equationHemonta Kumar Barman0Aly R. Seadawy1M. Ali Akbar2Dumitru Baleanu3Department of Applied Mathematics, University of Rajshahi, BangladeshDepartment of Mathematics, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia; Corresponding author.Department of Applied Mathematics, University of Rajshahi, BangladeshDepartment of Mathematics, Cankaya University, Ankara, Turkey; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan; Institute of Space Sciences, 077125 Magurele, RomaniaThe Riemann wave equation and the Novikov-Veselov equation are interesting nonlinear equations in the sphere of tidal and tsunami waves in ocean, river, ion and magneto-sound waves in plasmas, electromagnetic waves in transmission lines, homogeneous and stationary media etc. In this article, the generalized Kudryashov method is executed to demonstrate the applicability and effectiveness to extract travelling and solitary wave solutions of higher order nonlinear evolution equations (NLEEs) via the earlier stated equations. The technique is enucleated to extract solitary wave solutions in terms of trigonometric, hyperbolic and exponential function. We acquire bell shape soliton, consolidated bell shape soliton, compacton, singular kink soliton, flat kink shape soliton, smooth singular soliton and other types of soliton solutions by setting particular values of the embodied parameters. For the precision of the result, the solutions are graphically illustrated in 3D and 2D. The analytic solutions greatly facilitate the verification of numerical solvers on the stability analysis of the solution.http://www.sciencedirect.com/science/article/pii/S2211379720305301The nonlinear evolution equations (NLEEs)The generalized Kudryashov methodAnalytic solutionsThe Riemann wave equationThe Novikov-Veselov equationSolitary wave solutions |
| spellingShingle | Hemonta Kumar Barman Aly R. Seadawy M. Ali Akbar Dumitru Baleanu Competent closed form soliton solutions to the Riemann wave equation and the Novikov-Veselov equation Results in Physics The nonlinear evolution equations (NLEEs) The generalized Kudryashov method Analytic solutions The Riemann wave equation The Novikov-Veselov equation Solitary wave solutions |
| title | Competent closed form soliton solutions to the Riemann wave equation and the Novikov-Veselov equation |
| title_full | Competent closed form soliton solutions to the Riemann wave equation and the Novikov-Veselov equation |
| title_fullStr | Competent closed form soliton solutions to the Riemann wave equation and the Novikov-Veselov equation |
| title_full_unstemmed | Competent closed form soliton solutions to the Riemann wave equation and the Novikov-Veselov equation |
| title_short | Competent closed form soliton solutions to the Riemann wave equation and the Novikov-Veselov equation |
| title_sort | competent closed form soliton solutions to the riemann wave equation and the novikov veselov equation |
| topic | The nonlinear evolution equations (NLEEs) The generalized Kudryashov method Analytic solutions The Riemann wave equation The Novikov-Veselov equation Solitary wave solutions |
| url | http://www.sciencedirect.com/science/article/pii/S2211379720305301 |
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