分数阶klein-gordon-zakharov方程的新方法

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-08-18 DOI:10.1142/s0218348x23500950

Kang-le Wang

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引用次数: 1

摘要

Klein-Gordon-Zakharov方程是物理学中一个重要而有趣的模型。分数阶Klein-Gordon-Zakharov模型采用-导数来描述。利用分数阶有理数[公式:见文]-[公式:见文]方法和分数阶[公式:见文]方法，得到了一些新的孤波解。一些三维图形描述了这些新的孤立波解。本文的工作对其他相关类型的分数阶演化方程的研究具有重要的指导意义。

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NOVEL APPROACHES TO FRACTIONAL KLEIN–GORDON–ZAKHAROV EQUATION

The Klein–Gordon–Zakharov equation is an important and interesting model in physics. A fractional Klein–Gordon–Zakharov model is described by employing beta-derivative. Some new solitary wave solutions are acquired by utilizing the fractional rational [Formula: see text]–[Formula: see text] method and fractional [Formula: see text] method. Some 3D graphs are depicted to elaborate these new solitary wave solutions. The work is very helpful to study other related types of fractional evolution equations.

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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.