Two Kinds Of Eigenfunction Equations And Their Exact Solutions

The main work of this thesis contain two parts of content: I. by eliminating the potentials in the Lax pairs of the CMKdV equation,the first kind of eigenfunction equation is obtained, its Backlund transformation and exact solutions are also given. II.by using the Gauge transformation of the Lax pairs, the second kind of eigenfunction equation is presented. Further, with the help of Darboux transformation and Gauge transformation, the exact solutions of this kind of eigenfunction equation are obtained.