The Darboux Transformation Of The Derivative Manakov Equation And Its Explicit Solution

This paper studies mainly the Darboux transformation, which can obtain explicit solutions of nonlinear partial differential equations. In the first section of the paper, the basic theories of Darboux transformation and Darboux matrix are introduced. Based on this method, in the second section of the paper,we construct a DT of a coupled equation which is related to a 3×3 spectral problem. In the third section of the paper,we get from u₁= u₂ = v₁=v₂ = 0 the soliton solutins of the couple soliton equations, then we obtain the explicit solutions of the coupled equation. At last, the figures of the soliton solution are obtained by choosing the suitable parameters.