  A common challenge to proving asymptotic stability of solitary waves is
understanding the spectrum of the operator associated with the linearized flow.
The existence of eigenvalues can inhibit the dispersive estimates key to
proving stability. Following the work of Marzuola & Simpson, we prove the
absence of embedded eigenvalues for a collection of nonlinear Schrodinger
equations, including some one and three dimensional supercritical equations,
and the three dimensional cubic-quintic equation. Our results also rule out
nonzero eigenvalues within the spectral gap and, in 3D, endpoint resonances.
  The proof is computer assisted as it depends on the sign of certain inner
products which do not readily admit analytic representations. Our source code
is available for verification at
http://www.math.toronto.edu/simpson/files/spec_prop_asad_simpson_code.zip.
