<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

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

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"A general review on the NLS equation with point-concentrated nonlinearity"}

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...

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

Published Online: Oct 13, 2023

Page range: 62 - 84

Received: Apr 18, 2023

Accepted: Jul 28, 2023

DOI: https://doi.org/10.2478/caim-2023-0004

Keywords
NLS equation, concentrated nonlinearity, delta potentials, well-posedness, standing waves, stability, blow-up, point-like limit

© 2023 Lorenzo Tentarelli, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

Published Online: Oct 13, 2023

Page range: 62 - 84

Received: Apr 18, 2023

Accepted: Jul 28, 2023

DOI: https://doi.org/10.2478/caim-2023-0004

KeywordsNLS equation, concentrated nonlinearity, delta potentials, well-posedness, standing waves, stability, blow-up, point-like limit

© 2023 Lorenzo Tentarelli, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
NLS equation, concentrated nonlinearity, delta potentials, well-posedness, standing waves, stability, blow-up, point-like limit