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

Lorenzo Tentarelli

doi:10.2478/caim-2023-0004

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

Analysis of PDEs 2023-10-17 v2 Mathematical Physics math.MP

Authors: Lorenzo Tentarelli

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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.

Keywords

nls equation point-concentrated nonlinearity well-posedness standing waves blow-up analysis shrinking potentials

Cite

@article{arxiv.2304.09086,
  title  = {A general review on the NLS equation with point-concentrated nonlinearity},
  author = {Lorenzo Tentarelli},
  journal= {arXiv preprint arXiv:2304.09086},
  year   = {2023}
}

Comments

20 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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