In this paper, we study the dynamics of a class of nonlinear Schrödinger equation \( i u_t = \triangle u + u^p \) for \( x \in {\mathbb {T}}^d\). We prove that the PDE is integrable on the space of non-negative Fourier modes, in particular that each Fourier coefficient of a solution can be explicitly solved by quadrature. Within this subspace we demonstrate a large class of (quasi)periodic solutions all with the same frequency, as well as solutions which blowup in finite time in the \(L^2\) norm.