New Analysis Methods for the Coupled Fractional Nonlinear Hirota Equation

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-10-18 DOI:10.1142/s0218348x23501190

Kang-Le Wang

引用次数: 0

Abstract

In this work, the coupled fractional nonlinear Hirota equation is defined by using a powerful fractional derivative sense, which is M-truncate derivative. We explore the fractional functional method and fractional simple equation method to investigate the structure of the solutions of the coupled fractional nonlinear Hirota equations, and some new periodic solutions and solitary wave solutions are successfully acquired. The two proposed approaches are simple, effective and direct. Moreover, some 3D and 2D graphs are sketched to elaborate the behavior of these solutions. These obtained solitary wave and periodic solutions are helpful to improve the understanding of the physical behavior of the corresponding mathematical model.

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耦合分数阶非线性Hirota方程的新分析方法

本文利用一个强大的分数阶导数意义定义了耦合分数阶非线性Hirota方程，即m -截尾导数。利用分数阶泛函方法和分数阶简单方程方法研究了耦合分数阶非线性Hirota方程解的结构，成功地获得了一些新的周期解和孤波解。这两种方法简单、有效、直接。此外，还绘制了一些三维和二维图形来详细说明这些解的行为。这些孤波解和周期解有助于提高对相应数学模型物理行为的理解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fractals-Complex Geometry Patterns and Scaling in Nature and Society 数学-数学跨学科应用

CiteScore

7.40

自引率

23.40%

发文量

319

审稿时长

>12 weeks

期刊介绍： The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes. Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality. The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.