On the Structure of the Two-Soliton Interaction for the Korteweg–de Vries Equation

In this paper we consider an interaction of two solitons represented by a two-soliton solution of KdV. Unlike previous work on the subject we do not associate solitons with the maxima of the two-soliton solution but with the poles of a certain singular solution which can be considered as a two-antisoliton solution since it annihilates the original two-soliton solution. Motion of these poles may be chosen to represent motion of the solitons participating in the interaction and unlike interaction of the two maxima, interaction of the poles always proceeds in the same manner: The faster one approaches the slower one at a minimal distance, where they exchange identities and then separate