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Decay of KdV Solitons

In this paper we develop a linear eigenvalue decomposition for N-soliton solutions of the Korteweg--de Vries equation and use it to obtain a new mathematical explanation of two-soliton interaction in terms of particle decay. We discover 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.