In integrable systems, solitons are democratic. They collide, pass through each other, and emerge unchanged — same shape, same speed, same energy. The only trace of interaction is a phase shift. No soliton gains at another's expense. This is integrability's gift: exact balance between nonlinearity and dispersion preserves each wave's identity.
The Ostrovsky equation with anomalous dispersion is not integrable. Fariello et al. show what happens when soliton democracy breaks: the largest soliton eats the others.
Soliton interactions become inelastic. Energy transfers from smaller-amplitude solitons to the dominant one — the “soliton-champion” — in each collision. In a closed system, this produces progressive cannibalization: the champion grows while its rivals shrink, absorbing their energy through repeated unequal encounters. The population of solitons collapses toward a single dominant wave.
The solitons can still form trains and bound states, and some configurations show temporary recurrence reminiscent of the integrable KdV equation. But the recurrence is approximate and impermanent. The asymmetry introduced by non-integrability ensures that time favors concentration. Egalitarian coexistence degrades into winner-take-all hierarchy.
The structural point: integrability is what prevents hierarchy from forming among interacting waves. Remove it, and the same nonlinear interactions that sustain solitons also enable the strongest to exploit the weakest. The soliton-champion is not a different kind of wave — it is the same wave with a size advantage in a system where size advantages compound. Democracy requires exact symmetry; hierarchy is the generic outcome.