A multi-soliton solution of the DNLS equation based on pure Marchenko formalism

By means of some algebraic techniques, especially the Binet-Cauchy formula, an explicit multi-soliton solution of the derivative nonlinear Schrödinger equation with vanishing boundary condition is attained based on a pure Marchenko formalism without needing the usual scattering data except for given N simple poles. The one- and two-soliton solutions are given as two special examples in illustration of the general formula of multi-soliton solution. Their effectiveness and equivalence to other approaches are also demonstrated. Meanwhile, the asymptotic behavior of the multi-soliton solution is discussed in detail. It is shown that the N-soliton solution can be viewed as a summation of N one-soliton solutions with a definite displacement and phase shift of each soliton in the whole process (from t → ?∞ to t → +∞) of the elastic collisions.