Darboux Transformations of Zakharov I Equation

The Zakharov I (Z-I) equation is studied in the present paper. With the help of isomorphism of Lie algebra, its Lax pair which is presented by 3 × 3 matrices is mapped into the one described by 2 × 2 matrices. By the skills of theory of Darboux matrix, some Darboux transformations of Zakharov I equation are constructed in the present paper, and the relations between them are discussed. As an application, a soliton solution of Zakharov I equation is obtained.