Bilinear Equation of the Nonlinear Partial Differential Equation and Its Application
The homogeneous balance of undetermined coefficient method is firstly proposed to derive a more general bilinear equation of the nonlinear partial differential equation (NLPDE). By applying perturbation method, subsidiary ordinary differential equation (sub-ODE) method, and compatible condition to b...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/4912159 |
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| author | Xiao-Feng Yang Yi Wei |
| author_facet | Xiao-Feng Yang Yi Wei |
| author_sort | Xiao-Feng Yang |
| collection | DOAJ |
| description | The homogeneous balance of undetermined coefficient method is firstly proposed to derive a more general bilinear equation of the nonlinear partial differential equation (NLPDE). By applying perturbation method, subsidiary ordinary differential equation (sub-ODE) method, and compatible condition to bilinear equation, more exact solutions of NLPDE are obtained. The KdV equation, Burgers equation, Boussinesq equation, and Sawada-Kotera equation are chosen to illustrate the validity of our method. We find that the underlying relation among the G′/G-expansion method, Hirota’s method, and HB method is a bilinear equation. The proposed method is also a standard and computable method, which can be generalized to deal with other types of NLPDE. |
| format | Article |
| id | doaj-art-a92dfb81a2654c6bb76a9ab9666220ce |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-a92dfb81a2654c6bb76a9ab9666220ce2025-02-03T05:51:14ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/49121594912159Bilinear Equation of the Nonlinear Partial Differential Equation and Its ApplicationXiao-Feng Yang0Yi Wei1College of Science, Northwest A&F University, Yangling, 712100 Shaanxi, ChinaSchool of Medical Information Engineering, Jining Medical University, Rizhao 276826, ChinaThe homogeneous balance of undetermined coefficient method is firstly proposed to derive a more general bilinear equation of the nonlinear partial differential equation (NLPDE). By applying perturbation method, subsidiary ordinary differential equation (sub-ODE) method, and compatible condition to bilinear equation, more exact solutions of NLPDE are obtained. The KdV equation, Burgers equation, Boussinesq equation, and Sawada-Kotera equation are chosen to illustrate the validity of our method. We find that the underlying relation among the G′/G-expansion method, Hirota’s method, and HB method is a bilinear equation. The proposed method is also a standard and computable method, which can be generalized to deal with other types of NLPDE.http://dx.doi.org/10.1155/2020/4912159 |
| spellingShingle | Xiao-Feng Yang Yi Wei Bilinear Equation of the Nonlinear Partial Differential Equation and Its Application Journal of Function Spaces |
| title | Bilinear Equation of the Nonlinear Partial Differential Equation and Its Application |
| title_full | Bilinear Equation of the Nonlinear Partial Differential Equation and Its Application |
| title_fullStr | Bilinear Equation of the Nonlinear Partial Differential Equation and Its Application |
| title_full_unstemmed | Bilinear Equation of the Nonlinear Partial Differential Equation and Its Application |
| title_short | Bilinear Equation of the Nonlinear Partial Differential Equation and Its Application |
| title_sort | bilinear equation of the nonlinear partial differential equation and its application |
| url | http://dx.doi.org/10.1155/2020/4912159 |
| work_keys_str_mv | AT xiaofengyang bilinearequationofthenonlinearpartialdifferentialequationanditsapplication AT yiwei bilinearequationofthenonlinearpartialdifferentialequationanditsapplication |