分形介质中非线性枣金博柏原三和方程的新视角

Fractals Pub Date : 2024-04-12 DOI:10.1142/s0218348x2450066x
JIANSHE SUN
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引用次数: 0

摘要

本文首先创建了非光滑边界或微重力空间记录的分形Date-Jimbo-Kashiwara-Miwa(FDJKM)长波纹模型。利用分形半逆技术(FSIS)和分形行波变换(FTWT),我们得出了分形变分原理(FVP),并用 He Wierstrass 函数证明了强最小必要条件。我们发现了两种不同的孤波解,即双曲正割函数的平方形式和双曲正割函数形式。然后,通过 FVP 和最小稳态条件培育出孤子解。最后,解决了非光滑边界对孤子的影响,并通过三维等高线展示了解的特性。分形维度会影响波形,但不会影响其顶点值。利用技术展示孤子解(SWS)不仅值得称赞,而且值得关注。所采用的技术还可用于研究其他局部分数微积分偏微分方程的孤波解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A NEW PERSPECTIVE ON THE NONLINEAR DATE–JIMBO–KASHIWARA–MIWA EQUATION IN FRACTAL MEDIA

In this paper, we first created a fractal Date–Jimbo–Kashiwara–Miwa (FDJKM) long ripple wave model in a non-smooth boundary or microgravity space recorded. Using fractal semi-inverse skill (FSIS) and fractal traveling wave transformation (FTWT), the fractal variational principle (FVP) was derived, and the strong minimum necessary circumstance was attested with the He Wierstrass function. We have discovered two distinct solitary wave solutions, the square form of the hyperbolic secant function and the hyperbolic secant function form. Then, soliton solutions are cultivated through FVP and the minimum steady state condition. Finally, the influences of non-smooth boundaries on solitons were tackled, and the properties of the solution were demonstrated through three-dimensional contour lines. Fractal dimension can impact waveforms, but cannot affect their vertex values. The presentation of soliton solutions (SWS) using techniques is not only laudable but also noteworthy. The technique employed can also be used to investigate solitary wave solutions of other local fractional calculus partial differential equations.

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