Mohammad Mohammadi

In this paper, we present the complex sine-Gordon system as a nonlinear complex Klein–Gordon equation in1 1-dimensional space-time. Soliton-like solutions in the form of kinks (anti-kinks) and radiative profiles are two different soliton-like solutions that will be discussed in detail in this paper. Complex kinks (anti-kinks) are topological objects with zero electrical charges. Radiative profiles are new interesting objects that move at the speed of light and therefore have a vanishing rest mass. They can be either topological or non-topological and are created in kink–anti-kink collisions. They can have positive, negative, or vanishing electrical charges and produce a kink–anti-kink pair in high-energy collision processes. All soliton-like solutions satisfy the relativistic energy–momentum conservation relation as expected.