Application of the Homotopy Analysis Method for Solving the Variable Coefficient KdV-Burgers Equation
The homotopy analysis method is applied to solve the variable coefficient KdV-Burgers equation. With the aid of generalized elliptic method and Fourier’s transform method, the approximate solutions of double periodic form are obtained. These solutions may be degenerated into the approximate solution...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/309420 |
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| _version_ | 1832565449055797248 |
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| author | Dianchen Lu Jie Liu |
| author_facet | Dianchen Lu Jie Liu |
| author_sort | Dianchen Lu |
| collection | DOAJ |
| description | The homotopy analysis method is applied to solve the variable coefficient KdV-Burgers equation. With the aid of generalized elliptic method and Fourier’s transform method, the approximate solutions of double periodic form are obtained. These solutions may be degenerated into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. The results indicate that this method is efficient for the nonlinear models with the dissipative terms and variable coefficients. |
| format | Article |
| id | doaj-art-69bc48eee6aa4e11a7f5a0f0205d6f7c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-69bc48eee6aa4e11a7f5a0f0205d6f7c2025-02-03T01:07:46ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/309420309420Application of the Homotopy Analysis Method for Solving the Variable Coefficient KdV-Burgers EquationDianchen Lu0Jie Liu1Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, ChinaFaculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, ChinaThe homotopy analysis method is applied to solve the variable coefficient KdV-Burgers equation. With the aid of generalized elliptic method and Fourier’s transform method, the approximate solutions of double periodic form are obtained. These solutions may be degenerated into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. The results indicate that this method is efficient for the nonlinear models with the dissipative terms and variable coefficients.http://dx.doi.org/10.1155/2014/309420 |
| spellingShingle | Dianchen Lu Jie Liu Application of the Homotopy Analysis Method for Solving the Variable Coefficient KdV-Burgers Equation Abstract and Applied Analysis |
| title | Application of the Homotopy Analysis Method for Solving the Variable Coefficient KdV-Burgers Equation |
| title_full | Application of the Homotopy Analysis Method for Solving the Variable Coefficient KdV-Burgers Equation |
| title_fullStr | Application of the Homotopy Analysis Method for Solving the Variable Coefficient KdV-Burgers Equation |
| title_full_unstemmed | Application of the Homotopy Analysis Method for Solving the Variable Coefficient KdV-Burgers Equation |
| title_short | Application of the Homotopy Analysis Method for Solving the Variable Coefficient KdV-Burgers Equation |
| title_sort | application of the homotopy analysis method for solving the variable coefficient kdv burgers equation |
| url | http://dx.doi.org/10.1155/2014/309420 |
| work_keys_str_mv | AT dianchenlu applicationofthehomotopyanalysismethodforsolvingthevariablecoefficientkdvburgersequation AT jieliu applicationofthehomotopyanalysismethodforsolvingthevariablecoefficientkdvburgersequation |