Exact soliton solutions — collisions with phase shift only
The Toda lattice H = Σ p²/2 + e^{−(qₙ₊₁−qₙ)} is a rare completely integrable nonlinear system. Its exact N-soliton solutions are given by the τ-function method. Two solitons pass through each other with only a phase shift — no radiation, no deformation. The fast soliton gains a phase, the slow one loses it.