Soliton-like Solutions of the Complex Non-linear Klein-Gordon Systems in 1 + 1 Dimensions

Abstract

In this paper, we present soliton-like solutions of the non-linear complex Klein-Gordon systems in 1+1 dimensions. We will use polar representation to introduce three different soliton-like solutions including, complex kinks (anti-kinks), radiative profiles, and localized wave-packets. Complex kinks (anti-kinks) are topological objects with zero electrical charges. Radiative profiles are objects that move at the speed of light and therefore, have a zero rest mass. They can be created in kink-anti-kink collisions and vice versa. Localized wave packet solutions are non-topological objects for which wave and particle behavior are reconciled in a classical way. For localized wave packet solutions, the trivial initial phase imposes an uncertainty on the collision fates.