Darboux Transformation Of Nonlinear Equations And Explicit Solutions

The paper studies mainly the coupled mixed nonlinear schrodinger equation and L-C-Z equation. This paper can be divided into two parts. First, Darboux transforma-tion is used to derive explicit solutions of coupled mixed nonlinear schrodinger equation, when m=1and m=2. On the other hand, using the equivalent relation of L-C-Z spectral problem and AKNS spectral problem, explicit solutions of nonlinear L-C-Z equation are obtained from solutions of AKNS equation, and discussing on this.