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Nonlinear spectral singularities for confined nonlinearities

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We introduce a notion of spectral singularity that applies for a general class of nonlinear Schrodinger 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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American Physical Society (APS)

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Mathematics, Multidisciplinary

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Physical Review Letters 

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10.1103/PhysRevLett.110.260402

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