open access

https://hdl.handle.net/2115/97891

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

英語

Jacobi elliptic function

2025-06-07

Springer Nature

Partial Differential Equations and Applications

6(4)

In this paper, we study the large-time behavior of small solutions to the standard form of the systems of 1D cubic nonlinear Schr & ouml;dinger 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.

学術雑誌論文

Accepted Manuscript

This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/DOI:10.1007/s42985-025-00334-1

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