$\sigma_1$ and $\sigma_2$ automorphism of the systems of equations of   integrable hierarchies. Discrete and Backlund transformations
  It is shown that there exists two inner authomorpism which lead to different form of the sistems equations of integrable hierarchy. We present discrete and Backlund transformation connected with such systems and a general formula for multi-soliton solutions based on these symmetries. 
A. N. Leznov