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arXiv · 1303.2501

Nonlinear Spectral Singularities for Localized Nonlinearities

Ali Mostafazadeh
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Abstract

We introduce a notion of spectral singularity that applies for a general class of nonlinear Schreodinger 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 delta-function potential that is subject to a general confined nonlinearity.

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Ali Mostafazadeh. 2013-03-11. Nonlinear Spectral Singularities for Localized Nonlinearities. https://doi.org/10.1103/physrevlett.110.260402

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