On the nonlinear Schrödinger equations of derivative type

This paper studies the Cauchy problem both at finite and infinite times for a class of nonlinear Schrödinger equations with coupling of derivative type. The proof uses gauge transformations which reduce the original equations to systems of equations without coupling of derivative type. Concerning the Cauchy problem at finite times, we give sufficient conditions for the global well-posedness in the energy space. Concerning the Cauchy problem at infinity, we construct modified wave operators on small and sufficiently regular asymptotic states.