Nonlinear Interactions between Solitons in Complex<i>t</i>-Plane.I

Abstract

Nonlinear interactions between solitons for the Korteweg-de Vries and the Boussinesq equations are considered by extending analytically one of the independent variables into complex where soliton solutions can be discussed by using poles in the complex plane. It is found that there are three types of poles and that both collisions of solitons running in the same direction and head-on collisions can be well explained on the basis of the behavior of these poles.