Approximate Analytical and Numeric Solutions to a Forced Damped Gardner Equation
In this paper, some exact traveling wave solutions to the integrable Gardner equation are reported. The ansatz method is devoted for deriving some exact solutions in terms of Jacobi and Weierstrass elliptic functions. The obtained analytic solutions recover the solitary waves, shock waves, and cnoid...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2022/3240918 |
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| author | Alvaro H. Salas S. A. El-Tantawy Lorenzo J. Martinez H. |
| author_facet | Alvaro H. Salas S. A. El-Tantawy Lorenzo J. Martinez H. |
| author_sort | Alvaro H. Salas |
| collection | DOAJ |
| description | In this paper, some exact traveling wave solutions to the integrable Gardner equation are reported. The ansatz method is devoted for deriving some exact solutions in terms of Jacobi and Weierstrass elliptic functions. The obtained analytic solutions recover the solitary waves, shock waves, and cnoidal waves. Also, the relation between the Jacobi and Weierstrass elliptic functions is obtained. In the second part of this work, we derive some approximate analytic and numeric solutions to the nonintegrable forced damped Gardner equation. For the approximate analytic solutions, the ansatz method is considered. With respect to the numerical solutions, the evolution equation is solved using both the finite different method (FDM) and cubic B-splines method. A comparison between different approximations is reported. |
| format | Article |
| id | doaj-art-5e9b52254dba42ca8bd1a409d770e5a8 |
| institution | OA Journals |
| issn | 1537-744X |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-5e9b52254dba42ca8bd1a409d770e5a82025-08-20T02:05:09ZengWileyThe Scientific World Journal1537-744X2022-01-01202210.1155/2022/3240918Approximate Analytical and Numeric Solutions to a Forced Damped Gardner EquationAlvaro H. Salas0S. A. El-Tantawy1Lorenzo J. Martinez H.2Department of Mathematics and StatisticsDepartment of PhysicsUniversidad Nacional de ColombiaIn this paper, some exact traveling wave solutions to the integrable Gardner equation are reported. The ansatz method is devoted for deriving some exact solutions in terms of Jacobi and Weierstrass elliptic functions. The obtained analytic solutions recover the solitary waves, shock waves, and cnoidal waves. Also, the relation between the Jacobi and Weierstrass elliptic functions is obtained. In the second part of this work, we derive some approximate analytic and numeric solutions to the nonintegrable forced damped Gardner equation. For the approximate analytic solutions, the ansatz method is considered. With respect to the numerical solutions, the evolution equation is solved using both the finite different method (FDM) and cubic B-splines method. A comparison between different approximations is reported.http://dx.doi.org/10.1155/2022/3240918 |
| spellingShingle | Alvaro H. Salas S. A. El-Tantawy Lorenzo J. Martinez H. Approximate Analytical and Numeric Solutions to a Forced Damped Gardner Equation The Scientific World Journal |
| title | Approximate Analytical and Numeric Solutions to a Forced Damped Gardner Equation |
| title_full | Approximate Analytical and Numeric Solutions to a Forced Damped Gardner Equation |
| title_fullStr | Approximate Analytical and Numeric Solutions to a Forced Damped Gardner Equation |
| title_full_unstemmed | Approximate Analytical and Numeric Solutions to a Forced Damped Gardner Equation |
| title_short | Approximate Analytical and Numeric Solutions to a Forced Damped Gardner Equation |
| title_sort | approximate analytical and numeric solutions to a forced damped gardner equation |
| url | http://dx.doi.org/10.1155/2022/3240918 |
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