The orbital stability of elliptic solutions of the Focusing Nonlinear Schr\"{o}dinger Equation.

We examine the stability of the elliptic solutions of the focusing nonlinear Schr\"{o}dinger equation (NLS) with respect to subharmonic perturbations. Using the integrability of NLS, we discuss the spectral stability of the elliptic solutions. We show that the spectrally stable solutions are orbitally stable by constructing a Lyapunov functional using higher-order conserved quantities of NLS.