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ORIGINAL RESEARCH article

Front. Phys.
Sec. Interdisciplinary Physics
Volume 12 - 2024 | doi: 10.3389/fphy.2024.1526258
This article is part of the Research Topic Nonlinear Vibration and Instability in Nano/Micro Devices: Principles and Control Strategies View all 8 articles

Some novel exact solutions for the generalized time-space fractional coupled Hirota-Satsuma KdV equation

Provisionally accepted
Yueling Cheng Yueling Cheng *Siyuan Hong Siyuan Hong Shujun Yang Shujun Yang Xu Chi Xu Chi Jinghao Yang Jinghao Yang
  • Jiangsu University, Zhenjiang, China

The final, formatted version of the article will be published soon.

    In this paper, two efficient methods, namely the modified (G'/G,1/G) -expansion method and the G'/(bG'+G+a)-expansion method, are employed to obtain novel exact wave solutions for the generalized time-space fractional coupled Hirota-Satsuma KdV equation. Various types of analytical explicit solutions, including well-known bell-shape solitons, mixed solitary wave solutions, and periodic wave solutionsare obtained. These solutions are of great significance for revealing the nonlinear interaction between two long waves with different dispersion effects. The two-dimensional and three-dimensional distribution maps and contour plots corresponding to partial solutions are simulated to visually display the evolution process of relevant physical quantities over time. Moreover, the potential applications of these solutions in nano/micro devices and systems, especially in MEMS (Micro-Electro-Mechanical Systems)are discussed. It is demonstrated that the methods and processes utilized have strong applicability for constructing analytical solutions of nonlinear evolution equations.

    Keywords: time-space fractional coupled Hirota-Saturma KdV equation, the modified (G'/G,1/G)-expansion method, the G'/(bG'+G+a)-expansion method, blow-up, Analytical solutions

    Received: 11 Nov 2024; Accepted: 27 Nov 2024.

    Copyright: © 2024 Cheng, Hong, Yang, Chi and Yang. 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: Yueling Cheng, Jiangsu University, Zhenjiang, China

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