Kuznetsov–Ma rogue wave clusters of the nonlinear Schrödinger equation
<p dir="ltr">In this work, we investigate rogue wave (RW) clusters of different shapes, composed of Kuznetsov–Ma solitons (KMSs) from the nonlinear Schrödinger equation (NLSE) with Kerr nonlinearity. We present three classes of exact higher-order solutions on uniform background that...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | , , |
| Published: |
2023
|
| Subjects: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1864513530605076480 |
|---|---|
| author | Sarah Alwashahi (17785673) |
| author2 | Najdan B. Aleksić (14151444) Milivoj R. Belić (3958976) Stanko N. Nikolić (14151438) |
| author2_role | author author author |
| author_facet | Sarah Alwashahi (17785673) Najdan B. Aleksić (14151444) Milivoj R. Belić (3958976) Stanko N. Nikolić (14151438) |
| author_role | author |
| dc.creator.none.fl_str_mv | Sarah Alwashahi (17785673) Najdan B. Aleksić (14151444) Milivoj R. Belić (3958976) Stanko N. Nikolić (14151438) |
| dc.date.none.fl_str_mv | 2023-05-05T03:00:00Z |
| dc.identifier.none.fl_str_mv | 10.1007/s11071-023-08480-0 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/Kuznetsov_Ma_rogue_wave_clusters_of_the_nonlinear_Schr_dinger_equation/24995714 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Mathematical sciences Mathematical physics Pure mathematics Physical sciences Other physical sciences Nonlinear Schrödinger equation Rogue waves Kuznetsov–Ma rogue wave clusters Darboux transformation |
| dc.title.none.fl_str_mv | Kuznetsov–Ma rogue wave clusters of the nonlinear Schrödinger equation |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p dir="ltr">In this work, we investigate rogue wave (RW) clusters of different shapes, composed of Kuznetsov–Ma solitons (KMSs) from the nonlinear Schrödinger equation (NLSE) with Kerr nonlinearity. We present three classes of exact higher-order solutions on uniform background that are calculated using the Darboux transformation (DT) scheme with precisely chosen parameters. The first solution class is characterized by strong intensity narrow peaks that are periodic along the evolution x-axis, when the eigenvalues in DT scheme generate KMSs with commensurate frequencies. The second solution class exhibits a form of elliptical rogue wave clusters; it is derived from the first solution class when the first m evolution shifts in the nth-order DT scheme are nonzero and equal. We show that the high-intensity peaks built on KMSs of order n-2m periodically appear along the x-axis. This structure, considered as the central rogue wave, is enclosed by m ellipses consisting of a certain number of the first-order KMSs determined by the ellipse index and the solution order. The third class of KMS clusters is obtained when purely imaginary DT eigenvalues tend to some preset offset value higher than one, while keeping the x-shifts unchanged. We show that the central rogue wave at (0, 0) always retains its n - 2 m order. The n tails composed of the first-order KMSs are formed above and below the central maximum. When n is even, more complicated patterns are generated, with m and m - 1 loops above and below the central RW, respectively. Finally, we compute an additional solution class on a wavy background, defined by the Jacobi elliptic dnoidal function, which displays specific intensity patterns that are consistent with the background wavy perturbation. This work demonstrates an incredible power of the DT scheme in creating new solutions of the NLSE and a tremendous richness in form and function of those solutions.</p><h2>Other Information</h2><p dir="ltr">Published in: Nonlinear Dynamics<br>License: <a href="https://creativecommons.org/licenses/by/4.0" target="_blank">https://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1007/s11071-023-08480-0" target="_blank">https://dx.doi.org/10.1007/s11071-023-08480-0</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_035988acccb8d18a9670de5f41c3b9e4 |
| identifier_str_mv | 10.1007/s11071-023-08480-0 |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/24995714 |
| publishDate | 2023 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | Kuznetsov–Ma rogue wave clusters of the nonlinear Schrödinger equationSarah Alwashahi (17785673)Najdan B. Aleksić (14151444)Milivoj R. Belić (3958976)Stanko N. Nikolić (14151438)Mathematical sciencesMathematical physicsPure mathematicsPhysical sciencesOther physical sciencesNonlinear Schrödinger equationRogue wavesKuznetsov–Ma rogue wave clustersDarboux transformation<p dir="ltr">In this work, we investigate rogue wave (RW) clusters of different shapes, composed of Kuznetsov–Ma solitons (KMSs) from the nonlinear Schrödinger equation (NLSE) with Kerr nonlinearity. We present three classes of exact higher-order solutions on uniform background that are calculated using the Darboux transformation (DT) scheme with precisely chosen parameters. The first solution class is characterized by strong intensity narrow peaks that are periodic along the evolution x-axis, when the eigenvalues in DT scheme generate KMSs with commensurate frequencies. The second solution class exhibits a form of elliptical rogue wave clusters; it is derived from the first solution class when the first m evolution shifts in the nth-order DT scheme are nonzero and equal. We show that the high-intensity peaks built on KMSs of order n-2m periodically appear along the x-axis. This structure, considered as the central rogue wave, is enclosed by m ellipses consisting of a certain number of the first-order KMSs determined by the ellipse index and the solution order. The third class of KMS clusters is obtained when purely imaginary DT eigenvalues tend to some preset offset value higher than one, while keeping the x-shifts unchanged. We show that the central rogue wave at (0, 0) always retains its n - 2 m order. The n tails composed of the first-order KMSs are formed above and below the central maximum. When n is even, more complicated patterns are generated, with m and m - 1 loops above and below the central RW, respectively. Finally, we compute an additional solution class on a wavy background, defined by the Jacobi elliptic dnoidal function, which displays specific intensity patterns that are consistent with the background wavy perturbation. This work demonstrates an incredible power of the DT scheme in creating new solutions of the NLSE and a tremendous richness in form and function of those solutions.</p><h2>Other Information</h2><p dir="ltr">Published in: Nonlinear Dynamics<br>License: <a href="https://creativecommons.org/licenses/by/4.0" target="_blank">https://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1007/s11071-023-08480-0" target="_blank">https://dx.doi.org/10.1007/s11071-023-08480-0</a></p>2023-05-05T03:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1007/s11071-023-08480-0https://figshare.com/articles/journal_contribution/Kuznetsov_Ma_rogue_wave_clusters_of_the_nonlinear_Schr_dinger_equation/24995714CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/249957142023-05-05T03:00:00Z |
| spellingShingle | Kuznetsov–Ma rogue wave clusters of the nonlinear Schrödinger equation Sarah Alwashahi (17785673) Mathematical sciences Mathematical physics Pure mathematics Physical sciences Other physical sciences Nonlinear Schrödinger equation Rogue waves Kuznetsov–Ma rogue wave clusters Darboux transformation |
| status_str | publishedVersion |
| title | Kuznetsov–Ma rogue wave clusters of the nonlinear Schrödinger equation |
| title_full | Kuznetsov–Ma rogue wave clusters of the nonlinear Schrödinger equation |
| title_fullStr | Kuznetsov–Ma rogue wave clusters of the nonlinear Schrödinger equation |
| title_full_unstemmed | Kuznetsov–Ma rogue wave clusters of the nonlinear Schrödinger equation |
| title_short | Kuznetsov–Ma rogue wave clusters of the nonlinear Schrödinger equation |
| title_sort | Kuznetsov–Ma rogue wave clusters of the nonlinear Schrödinger equation |
| topic | Mathematical sciences Mathematical physics Pure mathematics Physical sciences Other physical sciences Nonlinear Schrödinger equation Rogue waves Kuznetsov–Ma rogue wave clusters Darboux transformation |