Extended (G′G)-expansion method for solving the coupled KdV equations with two arbitrary constants and its application to MEMS system
The coupled Korteweg-de Vries (cKdV) equations with two arbitrary constants hold significant importance in the field of micro-electro-mechanical systems (MEMS). These equations describe the behavior of nonlinear waves in MEMS devices. In MEMS applications, the cKdV equations can be used to analyze t...
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Frontiers Media S.A.
2025-05-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2025.1569291/full |
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| author | Jiao Zhang Fucai You |
| author_facet | Jiao Zhang Fucai You |
| author_sort | Jiao Zhang |
| collection | DOAJ |
| description | The coupled Korteweg-de Vries (cKdV) equations with two arbitrary constants hold significant importance in the field of micro-electro-mechanical systems (MEMS). These equations describe the behavior of nonlinear waves in MEMS devices. In MEMS applications, the cKdV equations can be used to analyze the dynamics of microstructures such as cantilevers, membranes, and resonators. By solving these equations, researchers can predict the behavior of MEMS devices under different operating conditions. In this paper, the (G′G)-expansion method is extended to seek more general travelling solutions of the cKdV equations with two arbitrary constants. The two arbitrary constants offer flexibility in modeling different physical phenomena and boundary conditions. As a result, many new and more general exact travelling wave solutions are obtained including soliton solutions, hyperbolic function solutions, trigonometric function solutions and rational solutions. They help in understanding the complex interactions between mechanical and electrical properties. Additionally, the study of these equations provides insights into the nonlinear behavior of MEMS systems, which is crucial for improving their performance and reliability. Overall, the cKdV equations with two arbitrary constants play a vital role in advancing the design and understanding of MEMS applications. |
| format | Article |
| id | doaj-art-c0abfb78361f499cb1e89e198fd6788f |
| institution | OA Journals |
| issn | 2296-424X |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Frontiers Media S.A. |
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| series | Frontiers in Physics |
| spelling | doaj-art-c0abfb78361f499cb1e89e198fd6788f2025-08-20T02:11:26ZengFrontiers Media S.A.Frontiers in Physics2296-424X2025-05-011310.3389/fphy.2025.15692911569291Extended (G′G)-expansion method for solving the coupled KdV equations with two arbitrary constants and its application to MEMS systemJiao ZhangFucai YouThe coupled Korteweg-de Vries (cKdV) equations with two arbitrary constants hold significant importance in the field of micro-electro-mechanical systems (MEMS). These equations describe the behavior of nonlinear waves in MEMS devices. In MEMS applications, the cKdV equations can be used to analyze the dynamics of microstructures such as cantilevers, membranes, and resonators. By solving these equations, researchers can predict the behavior of MEMS devices under different operating conditions. In this paper, the (G′G)-expansion method is extended to seek more general travelling solutions of the cKdV equations with two arbitrary constants. The two arbitrary constants offer flexibility in modeling different physical phenomena and boundary conditions. As a result, many new and more general exact travelling wave solutions are obtained including soliton solutions, hyperbolic function solutions, trigonometric function solutions and rational solutions. They help in understanding the complex interactions between mechanical and electrical properties. Additionally, the study of these equations provides insights into the nonlinear behavior of MEMS systems, which is crucial for improving their performance and reliability. Overall, the cKdV equations with two arbitrary constants play a vital role in advancing the design and understanding of MEMS applications.https://www.frontiersin.org/articles/10.3389/fphy.2025.1569291/fullextended (G′/G)-expansion methodnonlinear evolution equationscoupled KdV equationsmicro-electro-mechanical systemscomputerized mechanization |
| spellingShingle | Jiao Zhang Fucai You Extended (G′G)-expansion method for solving the coupled KdV equations with two arbitrary constants and its application to MEMS system Frontiers in Physics extended (G′/G)-expansion method nonlinear evolution equations coupled KdV equations micro-electro-mechanical systems computerized mechanization |
| title | Extended (G′G)-expansion method for solving the coupled KdV equations with two arbitrary constants and its application to MEMS system |
| title_full | Extended (G′G)-expansion method for solving the coupled KdV equations with two arbitrary constants and its application to MEMS system |
| title_fullStr | Extended (G′G)-expansion method for solving the coupled KdV equations with two arbitrary constants and its application to MEMS system |
| title_full_unstemmed | Extended (G′G)-expansion method for solving the coupled KdV equations with two arbitrary constants and its application to MEMS system |
| title_short | Extended (G′G)-expansion method for solving the coupled KdV equations with two arbitrary constants and its application to MEMS system |
| title_sort | extended g g expansion method for solving the coupled kdv equations with two arbitrary constants and its application to mems system |
| topic | extended (G′/G)-expansion method nonlinear evolution equations coupled KdV equations micro-electro-mechanical systems computerized mechanization |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2025.1569291/full |
| work_keys_str_mv | AT jiaozhang extendedggexpansionmethodforsolvingthecoupledkdvequationswithtwoarbitraryconstantsanditsapplicationtomemssystem AT fucaiyou extendedggexpansionmethodforsolvingthecoupledkdvequationswithtwoarbitraryconstantsanditsapplicationtomemssystem |