Comparison of solitons and waves

To simulate the soliton at this booth is used the numerical solution of the Korteweg - de Vries . It has the form:

[math]\dot U + UU' + CU''' = 0[/math].

For the numerical solution gradually find [math]U'[/math], [math]U''[/math] и [math]U'''[/math], using the central difference method:

[math]U' = \frac{U_{n+1} - U_{n-1}}{2\Delta x}[/math],

[math]U'' = \frac{U_{n+2} - 2U_{n} + U_{n-2}}{4\Delta x} \approx \frac{U_{n+1} - 2U_{n} + U_{n-1}}{2\Delta x}[/math],

[math]U''' = \frac{U_{n+2} - 2U_{n+1} + 2U_{n-1} - U_{n-2}}{4\Delta x}[/math].

At the stand of the initial moment of movement indicated by the purple outline of the soliton, turquoise gradient - moving waves.

Developer Tsvetkov Denis, when writing program code used by Alexander Yavorsky (ссылка).