The homogeneous balance of undetermined coefficients method and its application
The homogeneous balance of undetermined coefficients method is firstly proposed to solve such nonlinear partial differential equations (PDEs), the balance numbers of which are not positive integers. The proposed method can also be used to derive more general bilinear equation of nonlinear PDEs. The...
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De Gruyter
2016-01-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2016-0078 |
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doaj-bc94d2f4f20240f4a66929aaf35fa71f2021-09-06T19:20:08ZengDe GruyterOpen Mathematics2391-54552016-01-0114181682610.1515/math-2016-0078math-2016-0078The homogeneous balance of undetermined coefficients method and its applicationWei Yi0He Xin-Dang1Yang Xiao-Feng2Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, 710072, Shaanxi, ChinaSchool of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an, 710072, Shaanxi, ChinaCollege of Science, Northwest A&F University, Yangling 712100, Shaanxi, ChinaThe homogeneous balance of undetermined coefficients method is firstly proposed to solve such nonlinear partial differential equations (PDEs), the balance numbers of which are not positive integers. The proposed method can also be used to derive more general bilinear equation of nonlinear PDEs. The Eckhaus equation, the KdV equation and the generalized Boussinesq equation are chosen to illustrate the validity of our method. The proposed method is also a standard and computable method, which can be generalized to deal with some types of nonlinear PDEs.https://doi.org/10.1515/math-2016-0078homogeneous balance of undetermined coefficients methodbilinear equationeckhaus equationkdv equationgeneralized boussinesq equation35q5535q8035g25 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Wei Yi He Xin-Dang Yang Xiao-Feng |
| spellingShingle |
Wei Yi He Xin-Dang Yang Xiao-Feng The homogeneous balance of undetermined coefficients method and its application Open Mathematics homogeneous balance of undetermined coefficients method bilinear equation eckhaus equation kdv equation generalized boussinesq equation 35q55 35q80 35g25 |
| author_facet |
Wei Yi He Xin-Dang Yang Xiao-Feng |
| author_sort |
Wei Yi |
| title |
The homogeneous balance of undetermined coefficients method and its application |
| title_short |
The homogeneous balance of undetermined coefficients method and its application |
| title_full |
The homogeneous balance of undetermined coefficients method and its application |
| title_fullStr |
The homogeneous balance of undetermined coefficients method and its application |
| title_full_unstemmed |
The homogeneous balance of undetermined coefficients method and its application |
| title_sort |
homogeneous balance of undetermined coefficients method and its application |
| publisher |
De Gruyter |
| series |
Open Mathematics |
| issn |
2391-5455 |
| publishDate |
2016-01-01 |
| description |
The homogeneous balance of undetermined coefficients method is firstly proposed to solve such nonlinear partial differential equations (PDEs), the balance numbers of which are not positive integers. The proposed method can also be used to derive more general bilinear equation of nonlinear PDEs. The Eckhaus equation, the KdV equation and the generalized Boussinesq equation are chosen to illustrate the validity of our method. The proposed method is also a standard and computable method, which can be generalized to deal with some types of nonlinear PDEs. |
| topic |
homogeneous balance of undetermined coefficients method bilinear equation eckhaus equation kdv equation generalized boussinesq equation 35q55 35q80 35g25 |
| url |
https://doi.org/10.1515/math-2016-0078 |
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