Two solitons in KdV and KdV(2)

Two animations are shown together. Both show a wave number 3/2 soliton overtaking a wave number 1 soliton, but they evolve according to two different KdV equations.

The blue curve evolves according to KdV

u_t = \alpha u_{xx}
u_t = u_{3x}+6u u_x.

The red curve evolves according to KdV(2) u_{t_2} = u_{5x}+10+u u_{3x} +20 u_x u_{xx} +30 u^2 u_x.