On the asymptotic stability of ground states of the pure power NLS on the line at 3rd and 4th order Fermi Golden Rule

Scipio Cuccagna () and Masaya Maeda ()
Additional contact information
Scipio Cuccagna: University of Trieste
Masaya Maeda: Chiba University

Partial Differential Equations and Applications, 2025, vol. 6, issue 5, 1-42

Abstract: Abstract Assuming as hypotheses the results proved numerically by Chang et al. (SIAM J Math Anal 39:1070–1111, 2007/08) for the exponent $$p\in (3,5)$$ p ∈ ( 3 , 5 ) , we prove that some of the ground states of the nonlinear Schrödinger equation (NLS) with pure power nonlinearity of exponent p in the line are asymptotically stable for a certain set of values of the exponent p where the FGR occurs by means of a discrete mode 3rd or 4th order power interaction with the continuous mode. For the 3rd the result is true for generic p while for the 4th order case we assume that there are p’s satisfying Fermi Golden rule and the non-resonance condition of the threshold of the continuous spectrum of the linearization. The argument is similar to our recent result valid for p near 3 contained in Cuccagna and Maeda (J Funct Anal 288(11):110861, 2025).

Keywords: 35Q55 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s42985-025-00343-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:pardea:v:6:y:2025:i:5:d:10.1007_s42985-025-00343-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/42985/

DOI: 10.1007/s42985-025-00343-0

Access Statistics for this article

Partial Differential Equations and Applications is currently edited by Zhitao Zhang

More articles in Partial Differential Equations and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().