  This work deals with the focusing Nonlinear Schrodinger Equation in one
dimension with pure-power nonlinearity near cubic. We consider the spectrum of
the linearized operator about the soliton solution. When the nonlinearity is
exactly cubic, the linearized operator has resonances at the edges of the
essential spectrum. We establish the degenerate bifurcation of these resonances
to eigenvalues as the nonlinearity deviates from cubic. The leading-order
expression for these eigenvalues is consistent with previous numerical
computations.
