Exact Solutions of Damped Improved Boussinesq Equations by Extended (G′/G)-Expansion Method
With the help of the auxiliary function method, we solved the improved Boussinesq (IBq) equation with fluid dynamic damping and the modified IBq (IMBq) equation with Stokes damping, and we obtained their three types of travelling wave exact solutions, which is an extension service of the numerical s...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/4128249 |
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| author | Kai Fan Cunlong Zhou |
| author_facet | Kai Fan Cunlong Zhou |
| author_sort | Kai Fan |
| collection | DOAJ |
| description | With the help of the auxiliary function method, we solved the improved Boussinesq (IBq) equation with fluid dynamic damping and the modified IBq (IMBq) equation with Stokes damping, and we obtained their three types of travelling wave exact solutions, which is an extension service of the numerical simulation and the existence of a solution. From the waveform diagram of IBq equation with hydrodynamic damping, it can be seen that when the propagation velocity of kink wave changes, the amplitude also changes significantly, and it is also found that the kink isolated waveform is significantly asymmetric due to the increase of damping coefficient v, which may be of some value in explaining some physical phenomena. In addition, the symbolic computing software maple makes our computing work easier. |
| format | Article |
| id | doaj-art-000f4912049c41e1bd84b1854992b635 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-000f4912049c41e1bd84b1854992b6352025-02-03T01:00:08ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/41282494128249Exact Solutions of Damped Improved Boussinesq Equations by Extended (G′/G)-Expansion MethodKai Fan0Cunlong Zhou1Engineering Research Center of Heavy Machinery Ministry of Education, Taiyuan University of Science and Technology, Taiyuan 030024, ChinaEngineering Research Center of Heavy Machinery Ministry of Education, Taiyuan University of Science and Technology, Taiyuan 030024, ChinaWith the help of the auxiliary function method, we solved the improved Boussinesq (IBq) equation with fluid dynamic damping and the modified IBq (IMBq) equation with Stokes damping, and we obtained their three types of travelling wave exact solutions, which is an extension service of the numerical simulation and the existence of a solution. From the waveform diagram of IBq equation with hydrodynamic damping, it can be seen that when the propagation velocity of kink wave changes, the amplitude also changes significantly, and it is also found that the kink isolated waveform is significantly asymmetric due to the increase of damping coefficient v, which may be of some value in explaining some physical phenomena. In addition, the symbolic computing software maple makes our computing work easier.http://dx.doi.org/10.1155/2020/4128249 |
| spellingShingle | Kai Fan Cunlong Zhou Exact Solutions of Damped Improved Boussinesq Equations by Extended (G′/G)-Expansion Method Complexity |
| title | Exact Solutions of Damped Improved Boussinesq Equations by Extended (G′/G)-Expansion Method |
| title_full | Exact Solutions of Damped Improved Boussinesq Equations by Extended (G′/G)-Expansion Method |
| title_fullStr | Exact Solutions of Damped Improved Boussinesq Equations by Extended (G′/G)-Expansion Method |
| title_full_unstemmed | Exact Solutions of Damped Improved Boussinesq Equations by Extended (G′/G)-Expansion Method |
| title_short | Exact Solutions of Damped Improved Boussinesq Equations by Extended (G′/G)-Expansion Method |
| title_sort | exact solutions of damped improved boussinesq equations by extended g g expansion method |
| url | http://dx.doi.org/10.1155/2020/4128249 |
| work_keys_str_mv | AT kaifan exactsolutionsofdampedimprovedboussinesqequationsbyextendedggexpansionmethod AT cunlongzhou exactsolutionsofdampedimprovedboussinesqequationsbyextendedggexpansionmethod |