The Darboux Transformation And Explicit Solution Of A Soliton Equation Associated With ZI Equation

Darboux transformation plays an important role in soliton field. According to the DT theory, the transformation between solutions of nonlinear soliton equations can be easily obtained through finding the gauge transformation which keeps the corresponding Lax pairs unchanged, and the DT can be used repeatly to obtain a series of solutions of a soliton equation. Nowadays, many skills have been developed in DT theory to get the solutions of different soliton equations. The Darboux transformation of a (2+1)-dimensional soliton equationis obtained in this paper. This equation can be changed into the famous ZI equation through a simple transformation. First, the isomorphism of Lie algebras is used to map the Lax pair which is presented by 3 x 3 matrixinto the one which is presented by 2 x 2 matrixThen by using the skills in DT theory, the gauge transformation of the later spectral problem is constructed to give three relative Darboux transformations of the soliton equation,...