Exact solutions to the forced KdV equation via three efficient techniques

IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pramana Pub Date : 2024-06-07 DOI:10.1007/s12043-024-02774-7
Sanjaya K Mohanty, Md Sagib, Mohasena Ahmed
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Abstract

In this work, the exact travelling wave solutions to the forced Korteweg–de Vries (fKdV) equation with different force terms are studied with the help of symbolic computations. This equation is derived from a straightforward mathematical model that describes the behaviour of a shallow fluid layer when influenced by external forces. The fKdV equation has many applications in diverse fields, including fluid dynamics, plasma physics, soliton theory and mathematical physics, for modeling wave propagation and nonlinear phenomena under the influence of external forces. Solitary wave solutions for this equation have been derived using three distinct techniques: the extended \((G^\prime / G)\)-expansion method, the Kudryashov method and the \((1/G^\prime )\)-expansion method. As a result, several new solutions have been achieved which are in the form of hyperbolic, trigonometric, rational and exponential functions. Finally, the effects of different time-dependent external forces have been studied by presenting 3D, 2D and contour plots. It can be seen that the external forces affect the background and speed of solitary waves. The results could be expected to be helpful in understanding the propagation of solitary waves subjected to external forces.

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通过三种高效技术精确求解受迫 KdV 方程
在这项工作中,借助符号计算研究了带有不同力项的受迫 Korteweg-de Vries (fKdV) 方程的精确行波解。该方程源于一个简单明了的数学模型,用于描述浅层流体受外力影响时的行为。fKdV 方程在流体动力学、等离子物理学、孤子理论和数学物理学等多个领域都有广泛应用,用于模拟外力作用下的波传播和非线性现象。该方程的孤波解是通过三种不同的技术推导出来的:扩展的 \((G^\prime / G)\) 展开方法、库德里亚肖夫方法和 \((1/G^\prime )\) 展开方法。结果,得到了几种新的解,其形式包括双曲函数、三角函数、有理函数和指数函数。最后,我们通过三维、二维和等值线图研究了不同时间外力的影响。可以看出,外力会影响孤波的背景和速度。预计这些结果将有助于理解孤波在外力作用下的传播。
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来源期刊
Pramana
Pramana 物理-物理:综合
CiteScore
3.60
自引率
7.10%
发文量
206
审稿时长
3 months
期刊介绍: Pramana - Journal of Physics is a monthly research journal in English published by the Indian Academy of Sciences in collaboration with Indian National Science Academy and Indian Physics Association. The journal publishes refereed papers covering current research in Physics, both original contributions - research papers, brief reports or rapid communications - and invited reviews. Pramana also publishes special issues devoted to advances in specific areas of Physics and proceedings of select high quality conferences.
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