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

Embedded Eigenvalues and the Nonlinear Schrodinger Equation