分形修正KDV–ZAKHAROV–KUZNETSOV方程的广义变分结构

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-08-09 DOI:10.1142/s0218348x23500846

Kangkang Wang, Peng Xu

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引用次数: 5

摘要

对修正后的KdV–Zakharov–Kuznetsov方程进行了分形修正，并用半逆方法建立了其分形广义变分结构。此外，从另一个维场出发，通过两尺度变换对得到的分形广义变分结构进行了详细的讨论和验证。得到的分形广义变分结构通过分形空间中的能量形式揭示了守恒定律，可用于研究分形孤立波的性质。

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GENERALIZED VARIATIONAL STRUCTURE OF THE FRACTAL MODIFIED KDV–ZAKHAROV–KUZNETSOV EQUATION

A fractal modification of the modified KdV–Zakharov–Kuznetsov equation is suggested and its fractal generalized variational structure is established by means of the semi-inverse method. Furthermore, the obtained fractal generalized variational structure is discussed and verified through the two-scale transform from another dimension field in detail. The obtained fractal generalized variational structure reveals the conservation laws via the energy form in the fractal space and can be employed to study the fractal solitary wave properties.

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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.