Integrable nonlinear chain with exact soliton solutions
The Toda lattice (1967) is a chain of particles with exponential nearest-neighbor interactions: V(r) = e−r + r − 1. Despite being nonlinear, it is exactly integrable via the inverse scattering transform. Solitons — localized wave packets — pass through each other without distortion, emerging with only a phase shift. Faster solitons overtake slower ones; observe the elastic collision and phase shift. Energy and momentum are conserved exactly.