Partial classification of the large-time behavior of solutions to cubic nonlinear Schr\"odinger systems
In this paper, we study the large-time behavior of small solutions to the standard form of the systems of 1D cubic nonlinear Schr\"odinger equations consisting of two components and possessing a coercive mass-like conserved quantity. The cubic nonlinearity is known to be critical in one space d...
Saved in:
| Main Author | |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
31.12.2023
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | In this paper, we study the large-time behavior of small solutions to the
standard form of the systems of 1D cubic nonlinear Schr\"odinger 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 and
Sakoda, 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. |
|---|---|
| AbstractList | In this paper, we study the large-time behavior of small solutions to the
standard form of the systems of 1D cubic nonlinear Schr\"odinger 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 and
Sakoda, 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. |
| Author | Masaki, Satoshi |
| Author_xml | – sequence: 1 givenname: Satoshi surname: Masaki fullname: Masaki, Satoshi |
| BackLink | https://doi.org/10.48550/arXiv.2401.00478$$DView paper in arXiv |
| BookMark | eNqFjrsKwkAQRbfQwtcHWDnYG1dNML0oloKWQhjXSTKw2ZXZVfTvNWJvdYt74Jy-6jjvSKnxQidpnmV6jvLkR7JM9SLROl3nPVUdUCKjBWMxBC7ZYGTvwJcQawKLUtEsckNwoRof7KW9grf3FgsQPZj7hQ18VJYdocDR1HKe-iu7igTCK0RqwlB1S7SBRr8dqMlue9rsZ9-k4ibcoLyKNq34pq3-E29OfEeP |
| ContentType | Journal Article |
| Copyright | http://creativecommons.org/licenses/by/4.0 |
| Copyright_xml | – notice: http://creativecommons.org/licenses/by/4.0 |
| DBID | AKZ GOX |
| DOI | 10.48550/arxiv.2401.00478 |
| DatabaseName | arXiv Mathematics arXiv.org |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: GOX name: arXiv.org url: http://arxiv.org/find sourceTypes: Open Access Repository |
| DeliveryMethod | fulltext_linktorsrc |
| ExternalDocumentID | 2401_00478 |
| GroupedDBID | AKZ GOX |
| ID | FETCH-arxiv_primary_2401_004783 |
| IEDL.DBID | GOX |
| IngestDate | Mon Jan 08 05:49:27 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-arxiv_primary_2401_004783 |
| OpenAccessLink | https://arxiv.org/abs/2401.00478 |
| ParticipantIDs | arxiv_primary_2401_00478 |
| PublicationCentury | 2000 |
| PublicationDate | 2023-12-31 |
| PublicationDateYYYYMMDD | 2023-12-31 |
| PublicationDate_xml | – month: 12 year: 2023 text: 2023-12-31 day: 31 |
| PublicationDecade | 2020 |
| PublicationYear | 2023 |
| Score | 3.8091648 |
| SecondaryResourceType | preprint |
| Snippet | In this paper, we study the large-time behavior of small solutions to the
standard form of the systems of 1D cubic nonlinear Schr\"odinger equations
consisting... |
| SourceID | arxiv |
| SourceType | Open Access Repository |
| SubjectTerms | Mathematics - Analysis of PDEs |
| Title | Partial classification of the large-time behavior of solutions to cubic nonlinear Schr\"odinger systems |
| URI | https://arxiv.org/abs/2401.00478 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwdV1LSwMxEB7anryIolLfg3hdbTfZ7OYoYi2CD1BhD8KSZLNakG7ZbsWfbyZp1UuvyRCGmSTzMZl8A3DOqliVLGFRkrkrkLsTFEmpqJjKVIOsSodKUb7j_kGMX_ldnuQdwNVfGNV8T74CP7CeX7pwM7wgQsOsC904ppKt28c8PE56Kq6l_J-cw5h-6F-QGG3B5hLd4VVwxzZ07HQH3p_IPW7YEFKl0hxvDawrdOgLP6kWO6Ie77j6M09Tv3sC2xrNQk8MTgOthWrw2Xw0b2d16XNyGNiY57twOrp5uR5HXrViFngkCtK68FqzPei5NWwfcGBZprjQNhGMp9xoqdOylA62OWwipNiH_rpVDtZPHcIG9UkPDIVH0GubhT120bTVJ96kP-2feuE |
| link.rule.ids | 228,230,786,891 |
| linkProvider | Cornell University |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Partial+classification+of+the+large-time+behavior+of+solutions+to+cubic+nonlinear+Schr%5C%22odinger+systems&rft.au=Masaki%2C+Satoshi&rft.date=2023-12-31&rft_id=info:doi/10.48550%2Farxiv.2401.00478&rft.externalDocID=2401_00478 |