耦合碰撞-反作用 KdV 系统的变量公式

Fractals Pub Date : 2024-04-03 DOI:10.1142/s0218348x24500543
YINGZI GUAN, KHALED A. GEPREEL, JI-HUAN HE
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引用次数: 0

摘要

每一种浅水波都沿着分形边界传播,其数学模型无法用整数维精确表示。在本研究中,我们在变分理论框架内研究了一个沿不规则边界运动的分形-分形 KdV 耦合系统。然而,并不是每个分形-分数微分方程都能用变分原理来表述。事实证明,半反演法在为非线性问题寻找合适的变分原理以及消除所研究模型中的无关成分方面具有挑战性。我们考虑了具有任意系数的分形-分形 KdV 耦合系统,并建立了它的变分公式,从而揭示了模型的能量结构和各系数之间相互关系的非凡洞察力。该耦合 KdV 系统获得了令人鼓舞的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
VARIATIONAL FORMULATIONS FOR A COUPLED FRACTAL–FRACTIONAL KdV SYSTEM

Every shallow-water wave propagates along a fractal boundary, and its mathematical model cannot be precisely represented by integer dimensions. In this study, we investigate a coupled fractal–fractional KdV system moving along an irregular boundary within the framework of variational theory, which is commonly employed to derive governing equations. However, not every fractal–fractional differential equation can be formulated using variational principles. The semi-inverse method proves to be challenging in finding an appropriate variational principle for nonlinear problems and eliminating extraneous components from the studied model. We consider the coupled fractal–fractional KdV system with arbitrary coefficients and establish its variational formulation to unveil the remarkable insights into the energy structure of the model and interrelationships among coefficients. Encouraging results are obtained for this coupled KdV system.

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