Combined Damped Sinusoidal Oscillation Solutions to the (3 + 1)-D Variable-Coefficient Generalized NLW Equation in Liquid with Gas Bubbles
This paper investigates the combined damped sinusoidal oscillation solutions to the 3+1-D variable-coefficient (VC) generalized nonlinear wave equation. The bilinear form is considered in terms of Hirota derivatives. Accordingly, we utilize a binary Bell polynomial transformation for reducing the Co...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2022/8144911 |
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| author | Xiuwang Wang Jalil Manafian Wayan Eka Mahendra Azher M. Abed Mustafa Z. Mahmoud Guizhen Liang |
| author_facet | Xiuwang Wang Jalil Manafian Wayan Eka Mahendra Azher M. Abed Mustafa Z. Mahmoud Guizhen Liang |
| author_sort | Xiuwang Wang |
| collection | DOAJ |
| description | This paper investigates the combined damped sinusoidal oscillation solutions to the 3+1-D variable-coefficient (VC) generalized nonlinear wave equation. The bilinear form is considered in terms of Hirota derivatives. Accordingly, we utilize a binary Bell polynomial transformation for reducing the Cole-Hopf algorithm to get the exact solutions of the VC generalized NLW equation. The damped sinusoidal oscillations for two cases of the nonlinear wave ordinary differential equation will be studied. Using suitable mathematical assumptions, the novel kinds of solitary, periodic, and singular soliton solutions are derived and established in view of the trigonometric and rational functions of the governing equation. To achieve this, the illustrative example of the VC generalized nonlinear wave equation is provided to demonstrate the feasibility and reliability of the procedure used in this study. The trajectory solutions of the traveling waves are shown explicitly and graphically. The effect of the free parameters on the behavior of acquired figures of a few obtained solutions for two nonlinear rational exact cases was also discussed. By comparing the proposed method with the other existing methods, the results show that the execution of this method is concise, simple, and straightforward. |
| format | Article |
| id | doaj-art-2ae923c3e0d349f4a2fed2beaee4f6e3 |
| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-2ae923c3e0d349f4a2fed2beaee4f6e32025-02-03T01:20:16ZengWileyAdvances in Mathematical Physics1687-91392022-01-01202210.1155/2022/8144911Combined Damped Sinusoidal Oscillation Solutions to the (3 + 1)-D Variable-Coefficient Generalized NLW Equation in Liquid with Gas BubblesXiuwang Wang0Jalil Manafian1Wayan Eka Mahendra2Azher M. Abed3Mustafa Z. Mahmoud4Guizhen Liang5School of Mathematics and StatisticsDepartment of Applied MathematicsInstitut Pariwisata dan Bisnis InternasionalDepartment of Air Conditioning and RefrigerationDepartment of Radiology and Medical ImagingSchool of Mathematics and StatisticsThis paper investigates the combined damped sinusoidal oscillation solutions to the 3+1-D variable-coefficient (VC) generalized nonlinear wave equation. The bilinear form is considered in terms of Hirota derivatives. Accordingly, we utilize a binary Bell polynomial transformation for reducing the Cole-Hopf algorithm to get the exact solutions of the VC generalized NLW equation. The damped sinusoidal oscillations for two cases of the nonlinear wave ordinary differential equation will be studied. Using suitable mathematical assumptions, the novel kinds of solitary, periodic, and singular soliton solutions are derived and established in view of the trigonometric and rational functions of the governing equation. To achieve this, the illustrative example of the VC generalized nonlinear wave equation is provided to demonstrate the feasibility and reliability of the procedure used in this study. The trajectory solutions of the traveling waves are shown explicitly and graphically. The effect of the free parameters on the behavior of acquired figures of a few obtained solutions for two nonlinear rational exact cases was also discussed. By comparing the proposed method with the other existing methods, the results show that the execution of this method is concise, simple, and straightforward.http://dx.doi.org/10.1155/2022/8144911 |
| spellingShingle | Xiuwang Wang Jalil Manafian Wayan Eka Mahendra Azher M. Abed Mustafa Z. Mahmoud Guizhen Liang Combined Damped Sinusoidal Oscillation Solutions to the (3 + 1)-D Variable-Coefficient Generalized NLW Equation in Liquid with Gas Bubbles Advances in Mathematical Physics |
| title | Combined Damped Sinusoidal Oscillation Solutions to the (3 + 1)-D Variable-Coefficient Generalized NLW Equation in Liquid with Gas Bubbles |
| title_full | Combined Damped Sinusoidal Oscillation Solutions to the (3 + 1)-D Variable-Coefficient Generalized NLW Equation in Liquid with Gas Bubbles |
| title_fullStr | Combined Damped Sinusoidal Oscillation Solutions to the (3 + 1)-D Variable-Coefficient Generalized NLW Equation in Liquid with Gas Bubbles |
| title_full_unstemmed | Combined Damped Sinusoidal Oscillation Solutions to the (3 + 1)-D Variable-Coefficient Generalized NLW Equation in Liquid with Gas Bubbles |
| title_short | Combined Damped Sinusoidal Oscillation Solutions to the (3 + 1)-D Variable-Coefficient Generalized NLW Equation in Liquid with Gas Bubbles |
| title_sort | combined damped sinusoidal oscillation solutions to the 3 1 d variable coefficient generalized nlw equation in liquid with gas bubbles |
| url | http://dx.doi.org/10.1155/2022/8144911 |
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