One of the more important concepts used to understand partial differential equations is that of conserved quantities. One amazing result of preserving a particular conserved quantity is the Poincare Recurrence theorem; this theorem ensures the recurrence of the initial condition for any Hamiltonian system in finite dimensions.I have been studying the Nonlinear Schrodinger equation, a PDE with a preserved Hamiltonian in time, in preparation for studying a far less understood but similar nonlinear PDE. I will discuss recurrence, Hamiltonian preservation, and my strategies for better understanding recurrence patterns for certain initial conditions in NLS.