In this note we consider the Gross-Pitaevskii equation it+��+(12)=0, where is a complex-valued function defined on N, and study the following 2-parameters family of solitary waves: (x, t)=eitv(x1ct, x), where and x denotes the vector of the last N1 variables in N. We prove that every distribution solution , of the considered form, satisfies the following universal (and sharp) L-bound: This bound has two consequences. The first one is that is smooth and the second one is that a solution 0 exists, if and only if . We also prove a non-existence result for some solitary waves having finite energy. Some more general nonlinear Schrdinger equations are considered in the third and last section. The proof of our theorems is based on previous results of the author ([7]) concerning the Ginzburg-Landau system of equations in N.