Solitary waves travelling along an unsmooth boundary

被引：128
作者：
He, Ji-Huan [1 ,2 ,3 ]
Qie, Na [1 ]
He, Chun-Hui [4 ]
机构：
[1] Xian Univ Architecture & Technol, Sch Sci, Xian, Peoples R China
[2] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo, Henan, Peoples R China
[3] Soochow Univ, Coll Text & Clothing Engn, Natl Engn Lab Modern Silk, 199 Ren Ai Rd, Suzhou, Peoples R China
[4] Xian Univ Architecture & Technol, Sch Civil Engn, Xian 710055, Peoples R China
来源：
RESULTS IN PHYSICS | 2021年 / 24卷
关键词：
Solitary wave; Fractal derivative; Two-scale fractal; Fractal variational theory; FRACTAL CALCULUS; MODEL;
D O I：
10.1016/j.rinp.2021.104104
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
It is well-known that the boundary conditions will greatly affect the wave shape of a nonlinear wave equation. This paper reveals that the peak of a solitary wave is weakly affected by the unsmooth boundary. A fractal Korteweg-de Vries (KdV) equation is used as an example to show the solution properties of a solitary wave travelling along an unsmooth boundary. A fractal variational principle is established in a fractal space and its solitary wave solution is obtained, and its wave shape is discussed for different fractal dimensions of the boundary.
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页数：4
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