变分原理和分形复变在(3+1)维分形势-YTSF方程中的应用

Fractals Pub Date : 2024-01-23 DOI:10.1142/s0218348x24500270
Ju-Hong Lu
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引用次数: 0

摘要

本文重点对 (3+1) 维势能-Yu-Toda-Sasa-Fukuyama(YTSF)方程的分形修正进行数值研究。本文提出了一种基于二尺度分形复变和变分原理的变分方法来求解该分形方程。分形势-YTSF 方程可以通过分形复变转换为原始势-YTSF 方程。利用贺建奎提出的变分原理,提供了一些分形孤子型解法和分形周期波解法,这在现有文献中是没有的。此外,还对 Manafian 等人[East Asian J. Appl.给出了不同分形维数和振幅的分形波解的数值结果,以显示其传播行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
APPLICATION OF VARIATIONAL PRINCIPLE AND FRACTAL COMPLEX TRANSFORMATION TO (3+1)-DIMENSIONAL FRACTAL POTENTIAL-YTSF EQUATION
This paper focuses on the numerical investigation of the fractal modification of the (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation. A variational approach based on the two-scale fractal complex transformation and the variational principle is presented for solving this fractal equation. The fractal potential-YTSF equation can be transformed as the original potential-YTSF equation by means of the fractal complex transformation. Some fractal soliton-type solutions and fractal periodic wave solutions are provided by using the variational principle proposed by He, which are not touched in the existing literature. Some remarks about the variational formulation and the wave solutions for the original potential-YTSF equation by Manafian et al. [East Asian J. Appl. Math. 10(3) (2020) 549–565] are also given. Numerical results of the fractal wave solutions with different fractal dimensions and amplitudes are presented to show the propagation behavior.
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