On the Interaction of Nearly Equal Solitons in the KdV Equation

Abstract

An asymptotic formula is derived that describes the interaction of two solitons travelling with nearly equal speeds as the sum of two solitons with time-dependent parameters. If the difference in speeds is $O( \varepsilon )$, then this representation is valid to $O( {\varepsilon ^2 } )$ and describes the manner in which the solitons “bounce off” one another as well as giving asymptotic information on the minimum separation and the duration of the interaction.