Analytical approximate solutions for nonplanar Burgers equations by weighted residual method
In this work, analytical approximate progressive wave solutions for the generalized form of the nonplanar KdV-Burgers (KdV-B) and mKdV-Burgers (mKdV-B) equations are presented and the results are discussed. Motivated with the exact solutions of the planar KdV-B and mKdV-B equations, the weighted res...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2020-09-01
|
| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379720317605 |
| _version_ | 1818928853823782912 |
|---|---|
| author | H. Demiray E.R. El-Zahar |
| author_facet | H. Demiray E.R. El-Zahar |
| author_sort | H. Demiray |
| collection | DOAJ |
| description | In this work, analytical approximate progressive wave solutions for the generalized form of the nonplanar KdV-Burgers (KdV-B) and mKdV-Burgers (mKdV-B) equations are presented and the results are discussed. Motivated with the exact solutions of the planar KdV-B and mKdV-B equations, the weighted residual method is applied to propose analytical approximate solutions for the generalized form of the nonplanar KdV-B and mKdV-B equations. The structure of the KdV-B equation assumes a solitary wave type of solution, whereas the mKdV-B equation assumes a shock wave type of solution. The analytical approximate progressive wave solutions for the cylindrical(spherical) KdV-B and mKdV-B equations are obtained as some special cases and compared with numerical solutions and the results are depicted on 2D and 3D figures. The results revealed that both solutions are in good agreement. The advantage of the present method is that it is rather simple as compared to the inverse scattering method and gives the same results with the perturbative inverse scattering technique. Moreover, the present analytical solutions allow readers to carry out physical parametric studies on the behavior of the solution. In addition to the present solutions are defined overall the problem domain not only over the grid points, as well as the solution calculation has less CPU time-consuming and round-off error. |
| first_indexed | 2024-12-20T03:35:31Z |
| format | Article |
| id | doaj.art-1706fb99528747eea740c12835bdb131 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-20T03:35:31Z |
| publishDate | 2020-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-1706fb99528747eea740c12835bdb1312022-12-21T19:54:53ZengElsevierResults in Physics2211-37972020-09-0118103293Analytical approximate solutions for nonplanar Burgers equations by weighted residual methodH. Demiray0E.R. El-Zahar1Department of Mathematics, Faculty of Arts and Sciences, Isik University, 34980 Sile-Istanbul, TurkeyDepartment of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia; Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom, 32511, Egypt; Corresponding author at: Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia; Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom, 32511, Egypt.In this work, analytical approximate progressive wave solutions for the generalized form of the nonplanar KdV-Burgers (KdV-B) and mKdV-Burgers (mKdV-B) equations are presented and the results are discussed. Motivated with the exact solutions of the planar KdV-B and mKdV-B equations, the weighted residual method is applied to propose analytical approximate solutions for the generalized form of the nonplanar KdV-B and mKdV-B equations. The structure of the KdV-B equation assumes a solitary wave type of solution, whereas the mKdV-B equation assumes a shock wave type of solution. The analytical approximate progressive wave solutions for the cylindrical(spherical) KdV-B and mKdV-B equations are obtained as some special cases and compared with numerical solutions and the results are depicted on 2D and 3D figures. The results revealed that both solutions are in good agreement. The advantage of the present method is that it is rather simple as compared to the inverse scattering method and gives the same results with the perturbative inverse scattering technique. Moreover, the present analytical solutions allow readers to carry out physical parametric studies on the behavior of the solution. In addition to the present solutions are defined overall the problem domain not only over the grid points, as well as the solution calculation has less CPU time-consuming and round-off error.http://www.sciencedirect.com/science/article/pii/S2211379720317605Nonplanar KdV-B and mKdV-B equationsWeighted residual methodAnalytical approximate wave solution |
| spellingShingle | H. Demiray E.R. El-Zahar Analytical approximate solutions for nonplanar Burgers equations by weighted residual method Results in Physics Nonplanar KdV-B and mKdV-B equations Weighted residual method Analytical approximate wave solution |
| title | Analytical approximate solutions for nonplanar Burgers equations by weighted residual method |
| title_full | Analytical approximate solutions for nonplanar Burgers equations by weighted residual method |
| title_fullStr | Analytical approximate solutions for nonplanar Burgers equations by weighted residual method |
| title_full_unstemmed | Analytical approximate solutions for nonplanar Burgers equations by weighted residual method |
| title_short | Analytical approximate solutions for nonplanar Burgers equations by weighted residual method |
| title_sort | analytical approximate solutions for nonplanar burgers equations by weighted residual method |
| topic | Nonplanar KdV-B and mKdV-B equations Weighted residual method Analytical approximate wave solution |
| url | http://www.sciencedirect.com/science/article/pii/S2211379720317605 |
| work_keys_str_mv | AT hdemiray analyticalapproximatesolutionsfornonplanarburgersequationsbyweightedresidualmethod AT erelzahar analyticalapproximatesolutionsfornonplanarburgersequationsbyweightedresidualmethod |