KdV Solitons — Elastic Collision

Two solitons collide and emerge unchanged — only a phase shift remains. u_t + 6uu_x + u_xxx = 0

Speed c₁: 2.0 Speed c₂: 0.8 Anim speed:

u(x,t) = (c/2) sech²(√c/2 · (x−ct)) — exact soliton solution.
Top: current wave profile. Bottom: space-time diagram (brighter = larger amplitude). Notice the phase shift after collision.