Threshold Solutions For The 3d Cubic-quintic NLS
Abstract
We study the cubic-quintic NLS in three space dimensions. It is known that scattering holds for solutions with mass-energy in a region corresponding to positive virial, the boundary of which is delineated both by ground state solitons and by certain rescalings thereof. We classify the possible behaviors of solutions on the part of the boundary attained solely by solitons. In particular, we show that non-soliton solutions either scatter in both time directions or coincide (modulo symmetries) with a special solution, which scatters in one time direction and converges exponentially to the soliton in the other.
Recommended Citation
A. H. Ardila and J. Murphy, "Threshold Solutions For The 3d Cubic-quintic NLS," Communications in Partial Differential Equations, vol. 48, no. 5, pp. 819 - 862, Taylor and Francis Group; Taylor and Francis, Jan 2023.
The definitive version is available at https://doi.org/10.1080/03605302.2023.2212477
Department(s)
Mathematics and Statistics
Keywords and Phrases
Cubic-quintic NLS; Ground state; Scattering; Threshold solutions
International Standard Serial Number (ISSN)
1532-4133; 0360-5302
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2023 Taylor and Francis Group; Taylor and Francis, All rights reserved.
Publication Date
01 Jan 2023
