New promising and challenges of the fractional Calogero-Bogoyavlenskii-Schiff equation

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-10-14 DOI:10.1142/s0218348x23501104

Kang-Le Wang

引用次数: 0

Abstract

The Calogero–Bogoyavlenskii–Schiff equation is an important nonlinear evolution model to describe the propagation of Riemann waves. A fractional Calogero–Bogoyavlenskii–Schiff is described based on the conformable derivative for the first time. Some new soliton solutions are acquired with the aid of the extended fractional [Formula: see text] function method and fractional variable method. The two novel mathematical methods are very efficient and concise, which can also be utilized to solve other fractional evolution equations. Furthermore, these derived soliton solutions are illustrated by some 3D and 2D graphs with different fractal parameters and fractal dimensions, which might be helpful to study in plasma physics.

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分数阶Calogero-Bogoyavlenskii-Schiff方程的新前景与挑战

Calogero-Bogoyavlenskii-Schiff方程是描述黎曼波传播的一个重要的非线性演化模型。首次描述了基于可调导数的分数阶Calogero-Bogoyavlenskii-Schiff。利用扩展分数[公式:见文]函数法和分数变量法得到了一些新的孤子解。这两种新颖的数学方法简洁有效，也可用于求解其他分数阶演化方程。此外，我们还用不同分形参数和分形维数的三维和二维图形来说明这些推导出来的孤子解，这对等离子体物理的研究可能有所帮助。

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.