Partial classification of the large-time behavior of solutions to cubic nonlinear Schrödinger systems

Satoshi Masaki ()
Additional contact information
Satoshi Masaki: Hokkaido University

Partial Differential Equations and Applications, 2025, vol. 6, issue 4, 1-52

Abstract: Abstract In this paper, we study the large-time behavior of small solutions to the standard form of the systems of 1D cubic nonlinear Schrödinger equations consisting of two components and possessing a coercive mass-like conserved quantity. The cubic nonlinearity is known to be critical in one space dimension in view of the large-time behavior. By employing the result by Katayama-Sakoda (Partial Differ Equ Appl 1, 3(Paper No. 12):41 (2020). https://doi.org/10.1007/s42985-020-00012-4 ), one can obtain the large-time behavior of the solution if we can integrate the corresponding ODE system. We introduce an integration scheme suited to the system. The key idea is to rewrite the ODE system, which is cubic, as a quadratic system of quadratic quantities of the original unknown. By using this technique, we described the large-time behavior of solutions in terms of elementary functions and the Jacobi elliptic functions for several examples of standard systems.

Keywords: Nonlinear Schrödinger equation; System; Nonlinear ordinary differential system; Explicit solution of nonlinear ordinary differential system; Asymptotic behavior; Jacobi elliptic function; Primary 35Q55; Secondary 34A05; 34A34; 35B40 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s42985-025-00334-1 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:4:d:10.1007_s42985-025-00334-1

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

DOI: 10.1007/s42985-025-00334-1

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 ().