Some Traveling Wave Solutions to the Fifth-Order Nonlinear Wave Equation Using Three Techniques: Bernoulli Sub-ODE, Modified Auxiliary Equation, and G′/G-Expansion Methods
The fifth-order nonlinear wave equation contains terms involving higher-order spatial derivatives, such as uxxx and uxxxxx. These terms are responsible for dispersion, which affects the shape and propagation of the wave. The study of dispersion is important in many areas, including seismology, acous...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/7063620 |
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| author | Khalid K. Ali Maged Faihan Alotaibi Mohamed Omri M. S. Mehanna Abdel-Haleem Abdel-Aty |
| author_facet | Khalid K. Ali Maged Faihan Alotaibi Mohamed Omri M. S. Mehanna Abdel-Haleem Abdel-Aty |
| author_sort | Khalid K. Ali |
| collection | DOAJ |
| description | The fifth-order nonlinear wave equation contains terms involving higher-order spatial derivatives, such as uxxx and uxxxxx. These terms are responsible for dispersion, which affects the shape and propagation of the wave. The study of dispersion is important in many areas, including seismology, acoustics, and communication theory. In the current work, three potent analytical techniques are proposed in order to solve the fifth-order nonlinear wave equation. The used approaches are the modified auxiliary equation method, the Bernoulli Sub-ODE method, and the G′/G-expansion method (MAE). Some graphs are plotted to display our findings. The solutions to the nonlinear wave equation are used to describe the nonlinear dynamics of waves in physical systems. The results show how the dynamics of the wave solutions are influenced by the system parameters, which can be used as system controllers. The new approaches used in this work helped to find new solutions for traveling waves. This could be seen as a new contribution to the field. Water waves, plasma waves, and acoustic wave behavior can be described by the obtained solutions. |
| format | Article |
| id | doaj-art-31ca0a3fee514071b541d9adf1871b06 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-31ca0a3fee514071b541d9adf1871b062025-08-20T03:55:01ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/7063620Some Traveling Wave Solutions to the Fifth-Order Nonlinear Wave Equation Using Three Techniques: Bernoulli Sub-ODE, Modified Auxiliary Equation, and G′/G-Expansion MethodsKhalid K. Ali0Maged Faihan Alotaibi1Mohamed Omri2M. S. Mehanna3Abdel-Haleem Abdel-Aty4Mathematics DepartmentDepartment of PhysicsDeanship of Scientific Research (DSR)Faculty of EngineeringDepartment of PhysicsThe fifth-order nonlinear wave equation contains terms involving higher-order spatial derivatives, such as uxxx and uxxxxx. These terms are responsible for dispersion, which affects the shape and propagation of the wave. The study of dispersion is important in many areas, including seismology, acoustics, and communication theory. In the current work, three potent analytical techniques are proposed in order to solve the fifth-order nonlinear wave equation. The used approaches are the modified auxiliary equation method, the Bernoulli Sub-ODE method, and the G′/G-expansion method (MAE). Some graphs are plotted to display our findings. The solutions to the nonlinear wave equation are used to describe the nonlinear dynamics of waves in physical systems. The results show how the dynamics of the wave solutions are influenced by the system parameters, which can be used as system controllers. The new approaches used in this work helped to find new solutions for traveling waves. This could be seen as a new contribution to the field. Water waves, plasma waves, and acoustic wave behavior can be described by the obtained solutions.http://dx.doi.org/10.1155/2023/7063620 |
| spellingShingle | Khalid K. Ali Maged Faihan Alotaibi Mohamed Omri M. S. Mehanna Abdel-Haleem Abdel-Aty Some Traveling Wave Solutions to the Fifth-Order Nonlinear Wave Equation Using Three Techniques: Bernoulli Sub-ODE, Modified Auxiliary Equation, and G′/G-Expansion Methods Journal of Mathematics |
| title | Some Traveling Wave Solutions to the Fifth-Order Nonlinear Wave Equation Using Three Techniques: Bernoulli Sub-ODE, Modified Auxiliary Equation, and G′/G-Expansion Methods |
| title_full | Some Traveling Wave Solutions to the Fifth-Order Nonlinear Wave Equation Using Three Techniques: Bernoulli Sub-ODE, Modified Auxiliary Equation, and G′/G-Expansion Methods |
| title_fullStr | Some Traveling Wave Solutions to the Fifth-Order Nonlinear Wave Equation Using Three Techniques: Bernoulli Sub-ODE, Modified Auxiliary Equation, and G′/G-Expansion Methods |
| title_full_unstemmed | Some Traveling Wave Solutions to the Fifth-Order Nonlinear Wave Equation Using Three Techniques: Bernoulli Sub-ODE, Modified Auxiliary Equation, and G′/G-Expansion Methods |
| title_short | Some Traveling Wave Solutions to the Fifth-Order Nonlinear Wave Equation Using Three Techniques: Bernoulli Sub-ODE, Modified Auxiliary Equation, and G′/G-Expansion Methods |
| title_sort | some traveling wave solutions to the fifth order nonlinear wave equation using three techniques bernoulli sub ode modified auxiliary equation and g g expansion methods |
| url | http://dx.doi.org/10.1155/2023/7063620 |
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