Notes on “Different kinds of exact solutions with two-loop character of the two-component short pulse equations of the first kind”

• This paper focuses on the different kinds of periodic waves.
• The bifurcation of the traveling wave solutions is given.
• Some new periodic wave solutions are obtained.

The goal of this paper is to employ the approach of dynamical system to obtain the analytic expression for different kinds of periodic wave solutions of the two-component short pulse equations of the first kind: uxt=u+16(u3+3uv2)xx,vxt=v+16(v3+3u2v)xx, which are not obtained in Rui (2013) [20].