Darboux Transformation Of Some Soliton Equations

As one of the powerful tools for searching for the exact analytic solutions of soliton equations,Darboux transformation links two different solutions of the same equation.Therefore,resorting to Darboux transformation and trivial seed solutions for the soliton equations,we can obtain their nontrivial solutions.The present paper is devoted to investigating the Darboux transformation of the generalized multicomponent AKNS-type equation associated with a 33× matrix spectral problem,and then applying it to give solutions.First,the generation and development of solitons and the ideas of Darboux transformation are introduced.Second,with the help of the appropriate gauge transformation of the corresponding 33× matrix spectral problem,we construct three classes of N-order Darboux transformations for the generalized multicomponent AKNS-type equation.Based on these,we apply the three classes of 1-order Darboux transformations to get some nontrivial exact analytic solutions of generalized multicomponent AKNS-type equation from trivial seed solution.