Modular and Landen transformations between finite solutions of   Sine-Gordon Equation with phase N=1
  Among finite solutions of Sine-Gordon Equation with in phase N=1, we find Modular and Landen transformation between \theta representation and directly integrated solutions of breather and kink. Because of these transformations, we can say we unified the finite solutions of sine-Gordon equation with phase N=1. 
Nan-Hong Kuo and C. D. Hu
math-ph math.MP