The Cauchy problem for the nonlinear Schroedinger equation

The theorems of existence, uniqueness and continuous dependence upon the initial condition for the Cauchy problem are proved for the nonlinear Schroedinger equation. There is not a proposition that the solution tends to zero as the space variable tends to infinity in contrast to other papers. Only the continuity and boundedness of initial data and belonging of initial data derivatives to L2(R) are proposed