We study the focusing nonlinear Schrödinger equation,

\begin{equation}\label{eq:nls}\tag{\text{NLS}} \begin{cases} i u_t + \laplacian u = - |u|^{p-1} u,\\ u(x,0) = u_0(x), \end{cases} \end{equation}

as well as the focusing electromagnetic nonlinear Schrödinger equation

\begin{equation}\label{eq:emnls}\tag{\text{emNLS}} \begin{cases} i D_t u + \laplacian_A u = - |u|^{p-1} u,\\ u(x,0) = u_0(x), \end{cases} \end{equation}

with

\[ 0<\frac{N}{2}-\frac{2}{p-1}<1, \]

and for (emNLS) with certain potentials which decay at infinity. We obtain dichotomy results for (emNLS) for initial data below the ground state, and new scattering and blow up results above the ground state for (NLS). New methods include tools for studying the gradient of the modulus, ∇|u|, of the complex valued solutions of (NLS) and (emNLS) nonlinear bounds for H¹(R^N) functions lying below the ground state, and the analysis of function spaces with nonradial symmetry.