# zbMATH — the first resource for mathematics

Bi-dimensional soliton-like solutions of the nonlinear complex sine-Gordon system. (English) Zbl 1331.35080
Summary: In this paper, we present the complex sine-Gordon system as a nonlinear complex Klein-Gordon equation in $$1+1$$-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.

##### MSC:
 35C08 Soliton solutions 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 35Q51 Soliton equations
Full Text: