The Multiple Pole Solutions of the Sine-Gordon Equation

Abstract

The Sine-Gordon equation is studied in detail. In particular, the properties of the multiple pole solution are investigated. It is found that the multiple pole solution describes a weak bound state of solitons and antisolitions. The scatterings among soliton, breather and the multiple pole solution are examined explicitly. Further, it is shown that the position shift analysis gives useful informations on the dynamics of particle-like waves.