时空分数阶简化修正camassa-holm方程的分岔与精确解

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-08-08 DOI:10.1142/s0218348x23500858

Yan‐Chow Ma, Zenggui Wang

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引用次数: 0

摘要

利用分岔理论研究了时空分数阶简化修正Camassa-Holm (mCH)方程的精确行波解。在不同的参数条件下，得到了方程的相图。通过对不同轨道的分析，得到了方程的周期波、扭结、反扭结、爆发波、亮孤立解和暗孤立解。最后，对数值模拟和分数阶取对各种形式解的动力学行为的影响进行了解析讨论。

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BIFURCATION AND EXACT SOLUTIONS OF SPACE-TIME FRACTIONAL SIMPLIFIED MODIFIED CAMASSA–HOLM EQUATION

In this paper, exact traveling wave solutions of space-time fractional simplified modified Camassa–Holm (mCH) equation are investigated by the bifurcation theory. The phase portraits of the equation are obtained with different parameter conditions. By analyzing different orbits, periodic wave, kink, anti-kink, burst wave, bright and dark solitary solutions of the equation are acquired. Finally, numerical simulation and the effects of fractional order taking on the dynamic behaviors of various forms of solutions are analytically discussed.

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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.