The N-times Darboux Transformations Of The Coupled Derivative Manakov Equation And Its Exact Solutions

The paper studies mainly the N times Darboux transformation of an important soliton equation, that is coupled derivative Manakov equation,and its exact solution. There are four sections in this article. In the first section,the fundamental theory of the Darboux matrix and Darboux transformation are mainly introduced. In the second section,the coupled derivative Manakov equation which is related to a 3×3 spectral problem will be derived,and we will obtain 1 times Darboux transformation of the above spectral problem. In the third section, we get the N times Darboux transformation and provide the proof. In the forth section,we obtain the N-soliton solution of the soliton equation through the Darboux transformation and the seed solutions u₁ = u₂ = v₁ = v₂ = 0. Then we get the single soliton solution when N=l, and we plot several intersting figures of the solutions by choosing suitable parametres.