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Based on a revised version of inverse scattering transform for the derivative nonlinear Schrödinger (DNLS) equation with vanishing boundary condition (VBC), the explicit N-soliton solution has been derived by some algebra techniques of some special matrices and determinants, especially the Binet-Cauchy formula. The one- and two-soliton solutions have been given as the illustration of the general formula of the N-soliton solution. Moreover, the asymptotic behaviors of the N-soliton solution have been discussed. [ABSTRACT FROM AUTHOR]

In the inverse scattering transform (IST), the reflectionless Jost solutions are combined by their analytic properties in the complex spectrum parameter plane, and then can be shown to satisfy the two Lax equations indeed by Liouville theorem. So the corresponding soliton solutions certainly satisfy the nonlinear equation by compatibility condition. Especially the multi-soliton solutions of DNLS equation can be demonstrated in this way. [ABSTRACT FROM AUTHOR]

The inverse scattering transform for the nonlinear Schrödinger equation in normal dispersion with non-vanishing boundary values is re-examined using an affine parameter to avoid double-valued functions. An operable algebraic procedure is developed to evaluate dark multi-soliton solutions. The dark two-soliton solution is given explicitly as an example, and is verified by direct substitution. The additional motion of the soliton center is given by its asymptotic behavior. [ABSTRACT FROM AUTHOR]

Develops a Hamiltonian formalism for the nonlinear Schrodinger equation in physical space-time. Complexity of the first Lax equation and its variations with respect to canonical variables; Simplicity of the Poisson brackets of transition coefficients; Hamiltonian formalism in terms of action-angle variables.