title: Nonlinear spectral singularities for confined nonlinearities.
abstract: We introduce a notion of spectral singularity that applies for a general class of nonlinear Schrödinger operators involving a confined 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 δ-function potential that is subject to a general confined nonlinearity.
authors.affiliation: Department of Mathematics, Koç University, Istanbul, Turkey.
authors.forename: Ali
authors.initials: A
authors.lastname: Mostafazadeh