The Null Gauge Condition and the One Dimensional Nonlinear Schroedinger Equation with Cubic Nonlinearity Yoshio Tsutsumi Indiana University Mathematics Journal 1994 text pdf 10.1512/iumj.1994.43.43012 10.1512/iumj.1994.43.43012 en Indiana Univ. Math. J. 43 (1994) 241 - 254 state-of-the-art mathematics http://iumj.org/access/