Solitary waves travelling along an unsmooth boundary

• Published in: Results in physics Vol. 24; p. 104104
• Main Authors: He, Ji-Huan, Qie, Na, He, Chun-Hui
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-05-2021; Elsevier
• Subjects: Fractal derivative; Fractal variational theory; Solitary wave; Two-scale fractal; Solitary wave; Two-scale fractal; Fractal derivative; Fractal variational theory
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2021.104104

•A Hamilton-like fractal variational theory is established for a solitary wave.•The variational-based approach is used to solve the fractal solitary solutions.•The shape of fractal solitary wave is illustrated.
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.