# Comparison of solitons and waves

From Department of Theoretical and Applied Mechanics

To demonstrate a soliton propagation, we numerically solve the Korteweg–de Vries equation. It has the form:

- .

To obtain a numerical solution we successively calculate derivatives

, and , using the central difference method:- ,
- ,
- .

The soliton is indicated by the purple outline, the moving wave is shown by a turquoise gradient.

Coded by Tsvetkov Denis, the code written by Alexander Yavorsky (link) was used to accomplish the work.