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This work deals with the focusing Nonlinear Schrodinger Equation in onedimension with pure-power nonlinearity near cubic. We consider the spectrum ofthe linearized operator about the soliton solution. When the nonlinearity isexactly cubic, the linearized operator has resonances at the edges of theessential spectrum. We establish the degenerate bifurcation of these resonancesto eigenvalues as the nonlinearity deviates from cubic. The leading-orderexpression for these eigenvalues is consistent with previous numericalcomputations.

A Degenerate Edge Bifurcation in the 1D Linearized Nonlinear Schrodinger Equation

A Degenerate Edge Bifurcation in the 1D Linearized Nonlinear Schrodinger Equation