Darboux Transformations And Explicit Solutions For Two Soliton Equations

In this paper,we use the Darboux transformation to solve the derivative Schwarzian KdV equation and the sine-Gordon equation.First,the Darboux transformation for the linear spectral problems related to the derivative Schwarzian KdV equation is investigated,by which the explicit solutions of the equation are obtained.Further,we prove that the Darboux transformation is suitable for the sine-Gordon equation to give the explicit solutions.Besides,we polt figuers of these explicit solutions obtained by selecting the proper parameters.