THE FRACTAL ZAKHAROV–KUZNETSOV–BENJAMIN–BONA–MAHONY EQUATION: GENERALIZED VARIATIONAL PRINCIPLE AND THE SEMI-DOMAIN SOLUTIONS

Fractals Pub Date : 2024-05-23 DOI:10.1142/s0218348x24500798
KANG-JIA WANG, FENG SHI, SHUAI LI, PENG XU
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Abstract

By means of He’s fractal derivative, a new fractal (2 + 1)-dimensional Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation is extracted in this paper. The semi-inverse method is employed to establish the generalized fractal variational principle. The generalized fractal variational principle can show the conservation laws through the energy form in the fractal space. Moreover, some semi-domain solutions are also explored by applying the variational approach and the one-step method namely Wang’s direct mapping method-II. The dynamics of the extracted solutions on the Cantor set are unveiled graphically. The findings of this study are expected to provide some new insights into the exploration of the fractal PDEs.

分形扎哈罗夫-库兹涅佐夫-本杰明-博纳-马霍尼方程:广义变分原理和半域解
通过 He 的分形导数,本文提取了一个新的分形 (2 + 1) 维扎哈罗夫-库兹涅佐夫-本杰明-博纳-马霍尼方程。本文采用半逆方法建立了广义分形变分原理。广义分形变分原理可以在分形空间中通过能量形式显示守恒定律。此外,还应用变分法和一步法(即王氏直接映射法-II)探索了一些半域解。提取的解在康托尔集上的动态变化以图形的形式展现出来。本研究的发现有望为分形多项式的探索提供一些新的见解。
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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