Eigenfunction Equations Of Soliton Equations And Their B(a|")cklund Transformation

On the basis of Lax pairs and Darboux transformation of two half discrete soliton equations, we obtained two (1+1)-and a (2+1)-dimensional eigenfunction equations. Further more, we prove that the gauge transformation of the Lax pairs is a Backlund transformation of eigenfunction equation. Finally, with the aid of Backlund transformation, the exact solutions of eigenfunction equations are given.