A Family of Interesting Exact Solutions of the Sine-Gordon Equation

By using AKNS Phys. Rev. Lett. 31 (1973) 125 system and introducing the wave function, a family of interesting exact solutions of the sine-Gordon equation are constructed. These solutions seem to be some soliton, kink, and anti-kink ones respectively for the different choice of the spectrum, whereas due to the interaction between two traveling-waves they have some properties different from usual soliton, kink, and anti-kink solutions.