Decay of KDV solitons

A linear eigenvalue decomposition for N-soliton solutions of the Korteweg-de Vries equation was developed. The decomposition was used to obtain a new mathematical explanation of two-soliton interaction in terms of particle decay. It was discovered that the two-soliton 'particles' or pulses which appear in each solution exchange identities upon collision and emit a dual 'ghost' particle pair in order to conserve mass and momentum.