Quantum mechanics

Korteweg–de Vries equation

Boundary (topology)

Boundary value problem

Operating system

Computer science

Classical mechanics

Fractal

Physics

Nonlinear system

Mathematics

Fractal dimension

Mathematical analysis

Fractal analysis

Fractal derivative

Space (punctuation)

Results in Physics

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.

Solitary waves travelling along an unsmooth boundary