Korteweg–de Vries equation: uₜ + 6uuₓ + uₓₓₓ = 0 — solitons pass through each other unchanged
Soliton 1 (fast)
Soliton 2 (slow)
Exact 2-soliton solution: Taller solitons travel faster (v=2A), so the fast one overtakes the slow one. Despite nonlinear interaction, each soliton emerges with original shape and speed — only a phase shift remains. This elasticity, discovered by Zabusky-Kruskal 1965, launched soliton physics.