On the existence of certain elliptic solutions of the cubically nonlinear Schrödinger equation

We consider solutions of the cubically nonlinear Schrödinger equation. For a certain class of solutions of the form \(\Psi(t,z)=(f(t,z)+id(z))e^{i\phi(z)}\) with \(f,\phi,d\in\mathbb{R}\) , we prove that they are nonexistent in the general case \(f_z\neq 0\) , \(f_t\neq 0\) , \(d_z\neq 0\) . In the three nongeneric cases ( \(f_z\neq 0\) ), ( \(f_t\neq 0\) , \(f_t=0\) , \(d_z=0\) ), and ( \(f_z=0\) , \(f_t\neq 0\) ), we present a two-parameter set of solutions, for which we find the constraints specifying real bounded and unbounded solutions.