1303.2501 (Ali Mostafazadeh)

Nonlinear Spectral Singularities for Localized Nonlinearities    [PDF]

Ali Mostafazadeh

We generalize the notion of a spectral singularity for a class of nonlinear Schrodinger operators involving a localized nonlinearity. The presence of the nonlinearity does not break the parity-reflection symmetry of spectral singularities but makes them amplitude-dependent. Nonlinear spectral singularities are, therefore, associated with a resonance effect that produces amplified waves with a specific amplitude-wavelength profile. We explore the consequences of this phenomenon for a complex delta-function potential that is subject to a general localized nonlinearity.

View original: http://arxiv.org/abs/1303.2501