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ORIGINAL RESEARCH article
Front. Phys.
Sec. Interdisciplinary Physics
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1569291
This article is part of the Research TopicNonlinear Vibration and Instability in Nano/Micro Devices: Principles and Control StrategiesView all 16 articles
Extended ( G ′ G )-expansion method for solving the coupled KdV equations with two arbitrary constants and its application to MEMS system
Provisionally accepted- Shenyang Institute of Engineering, Shenyang, China
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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.G )-expansion method, nonlinear evolution equations, coupled KdV equations, microelectro-mechanical systems, computerized mechanization
Keywords: extended $(\frac{G'}{G})$-expansion method, Nonlinear evolution equations, coupled KdV equations, Micro-electro-mechanical systems, computerized mechanization
Received: 31 Jan 2025; Accepted: 08 Apr 2025.
Copyright: © 2025 Zhang and You. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Jiao Zhang, Shenyang Institute of Engineering, Shenyang, China
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