New Solitary-Wave Solutions of the Van der Waals Normal Form for Granular Materials via New Auxiliary Equation Method
In this paper, we use general Riccati equation to construct new solitary wave solutions of the Van der Waals normal form, which is one of the most famous models for natural and industrial granular materials. It is very important to understand the static and dynamic characteristics of this models in...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/15/2560 |
| _version_ | 1797413219721019392 |
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| author | Xiaomeng Zhu Jinkang Cheng Zhuokai Chen Guojiang Wu |
| author_facet | Xiaomeng Zhu Jinkang Cheng Zhuokai Chen Guojiang Wu |
| author_sort | Xiaomeng Zhu |
| collection | DOAJ |
| description | In this paper, we use general Riccati equation to construct new solitary wave solutions of the Van der Waals normal form, which is one of the most famous models for natural and industrial granular materials. It is very important to understand the static and dynamic characteristics of this models in many application fields. We solve the general Riccati equation through different function transformation, and many new hyperbolic function solutions are obtained. Then, it is substituted into the Van der Waals normal form as an auxiliary equation. Abundant types of solitary-wave solutions are obtained by choosing different coefficient in the general Riccati equation, and some of them have not been found in other documents. The results show that the analysis method we used is very simple and effective for dealing with nonlinear models. |
| first_indexed | 2024-03-09T05:14:29Z |
| format | Article |
| id | doaj.art-e6eaf0dcc4d64f56b86bad8970c3994a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:14:29Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e6eaf0dcc4d64f56b86bad8970c3994a2023-12-03T12:47:07ZengMDPI AGMathematics2227-73902022-07-011015256010.3390/math10152560New Solitary-Wave Solutions of the Van der Waals Normal Form for Granular Materials via New Auxiliary Equation MethodXiaomeng Zhu0Jinkang Cheng1Zhuokai Chen2Guojiang Wu3Hefei No. 8 High School, Hefei 230071, ChinaHefei No. 8 High School, Hefei 230071, ChinaHefei No. 8 High School, Hefei 230071, ChinaInstitute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, ChinaIn this paper, we use general Riccati equation to construct new solitary wave solutions of the Van der Waals normal form, which is one of the most famous models for natural and industrial granular materials. It is very important to understand the static and dynamic characteristics of this models in many application fields. We solve the general Riccati equation through different function transformation, and many new hyperbolic function solutions are obtained. Then, it is substituted into the Van der Waals normal form as an auxiliary equation. Abundant types of solitary-wave solutions are obtained by choosing different coefficient in the general Riccati equation, and some of them have not been found in other documents. The results show that the analysis method we used is very simple and effective for dealing with nonlinear models.https://www.mdpi.com/2227-7390/10/15/2560Riccati equationVan der Waals normal formnonlinear evolution equationsolitary wave solutionauxiliary equation |
| spellingShingle | Xiaomeng Zhu Jinkang Cheng Zhuokai Chen Guojiang Wu New Solitary-Wave Solutions of the Van der Waals Normal Form for Granular Materials via New Auxiliary Equation Method Mathematics Riccati equation Van der Waals normal form nonlinear evolution equation solitary wave solution auxiliary equation |
| title | New Solitary-Wave Solutions of the Van der Waals Normal Form for Granular Materials via New Auxiliary Equation Method |
| title_full | New Solitary-Wave Solutions of the Van der Waals Normal Form for Granular Materials via New Auxiliary Equation Method |
| title_fullStr | New Solitary-Wave Solutions of the Van der Waals Normal Form for Granular Materials via New Auxiliary Equation Method |
| title_full_unstemmed | New Solitary-Wave Solutions of the Van der Waals Normal Form for Granular Materials via New Auxiliary Equation Method |
| title_short | New Solitary-Wave Solutions of the Van der Waals Normal Form for Granular Materials via New Auxiliary Equation Method |
| title_sort | new solitary wave solutions of the van der waals normal form for granular materials via new auxiliary equation method |
| topic | Riccati equation Van der Waals normal form nonlinear evolution equation solitary wave solution auxiliary equation |
| url | https://www.mdpi.com/2227-7390/10/15/2560 |
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