Multiple Soliton Solutions for Coupled Modified Korteweg–de Vries (mkdV) with a Time-Dependent Variable Coefficient

IF 2.2 3区 综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES Symmetry-Basel Pub Date : 2023-10-25 DOI:10.3390/sym15111972
Haroon D. S. Adam, Khalid I. A. Ahmed, Mukhtar Yagoub Youssif, Marin Marin
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Abstract

In this manuscript, we implement analytical multiple soliton wave and singular soliton wave solutions for coupled mKdV with a time-dependent variable coefficient. Based on the similarity transformation and Hirota bilinear technique, we construct both multiple wave kink and wave singular kink solutions for coupled mKdV with a time-dependent variable coefficient. We implement the Hirota bilinear technique to compute analytical solutions for the coupled mKdV system. Such calculations are made by using a software with symbolic computation software, for instance, Maple. Recently some researchers used Maple in order to show that the bilinear method of Hirota is a straightforward technique which can be used in the approach of differential, nonlinear models. We analyzed whether the experiments proved that the procedure is effective and can be successfully used for many other mathematical models used in physics and engineering. The results of this study display that the profiles of multiple-kink and singular-kink soliton types can be efficiently controlled by selecting the particular form of a similar time variable. The changes in the solitons based on the changes in the arbitrary function of time allows for more applications of them in applied sciences.
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时变系数耦合修正Korteweg-de Vries (mkdV)的多孤子解
在本文中,我们实现了具有时变系数的耦合mKdV的多孤子波和奇异孤子波解析解。基于相似变换和Hirota双线性技术,构造了具有时变系数的耦合mKdV的多重波扭结解和波奇异扭结解。我们实现了Hirota双线性技术来计算耦合mKdV系统的解析解。这种计算是通过使用符号计算软件,如Maple软件来完成的。最近一些研究者使用Maple来证明Hirota的双线性方法是一种简单的技术,可以用于微分、非线性模型的处理。我们分析了实验是否证明该方法是有效的,并且可以成功地用于物理和工程中使用的许多其他数学模型。研究结果表明,通过选择相似时间变量的特定形式,可以有效地控制多扭结和单扭结孤子类型的轮廓。随着任意时间函数的变化,孤子的变化使得它们在应用科学中有了更多的应用。
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来源期刊
Symmetry-Basel
Symmetry-Basel MULTIDISCIPLINARY SCIENCES-
CiteScore
5.40
自引率
11.10%
发文量
2276
审稿时长
14.88 days
期刊介绍: Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.
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