Prolongation Approach to B\"{a}cklund Transformation of   Zhiber-Mikhailov-Shabat Equation
  The prolongation structure of Zhiber-Mikhailov-Shabat (ZMS) equation is studied by using Wahlquist-Estabrook's method. The Lax-pair for ZMS equation and Riccati equations for pseudopotentials are formulated respectively from linear and nonlinear realizations of the prolongation structure. Based on nonlinear realization of the prolongation structure, an auto-B$\ddot{a}$cklund transformation of ZMS equation is obtained. 
Huan-xiong Yang and You-Quan Li