Two-soliton collision on the Korteweg–de Vries equation: u_t + 6uu_x + u_xxx = 0. Solitons pass through each other elastically — shape preserved, only a phase shift remains. Adjust amplitudes and initial separation.
The exact two-soliton solution uses the inverse scattering transform. Each soliton has speed c = 2a² (amplitude determines velocity — taller solitons travel faster). After collision the solitons emerge unchanged, demonstrating perfect elasticity — a hallmark of integrable PDEs.