Finite energy solutions of nonlinear Schrdinger equations of derivative type

This paper is concerned with the initial value problem for nonlinear Schrodinger equations of the form where 8 = 8z = 8 / 8:i:1 ..\, A1, ..\2 E Iffi., and 2 ;£ Pl E H1(Iffi.) and then there exists a unique global solution 'Ip of ( *) such that In this paper we introduce a new method to obtain the result. Key words. Derivative Nonlinear Schrodinger Equations, Gauge Transformations. AMS(MOS) subject classifications. 35Q55, 35Q60