Simulation of Zbusky & Kruskal

Zabusky & Kruskal の KdV 方程式の数値シュミレーション

Zabusky & Kruskal (1965)

KdV equation:

$u_t+u u_x+delta^2u_{xxx}=0$ ,
where u = u ( x, t ) and delta

=0.022.

1 soliton solution:

$u=u_oo+(u_0-u_oo)sech^2(x-x_0)/Delta, Delta=12delta/(u_0-u_oo)^{1/2}$ ,

Boundary condition: u ( x + L, t ) = u ( x, t ).

Numerical scheme of KdV equation:

,
where i = 0, 1, ..., N-1,

and

Parameters: , , N=128 and L=2.

シュミレーション

The source.

参考文献

[1] N. J. Zabusky and M. D. Kruskal: Integration of "solitons" in a collisionless plasma and recurrence of initial states, Phys. Rev. Lett. 15 (1965), 240--243.