A general review on the NLS equation with point-concentrated nonlinearity

Abstract

The paper presents a complete (to the best of the author's knowledge) overview on the existing literature concerning the NLS equation with point-concentrated nonlinearity. Precisely, it mainly covers the following topics: definition of the model, weak and strong local well-posedness, global well-posedness, classification and stability (orbital and asymptotic) of the standing waves, blow-up analysis and derivation from the standard NLS equation with shrinking potentials. Also some related problem is mentioned.

arXiv comment20 pages. Keywords: NLS equation, concentrated nonlinearity, delta potentials, well-posedness, standing waves, stability, blow-up, point-like limit. Minor revisions made with respect to the previous version

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Cited by in corpus (1)

• Nonlinear scalar field equation with point interaction