Symmetry Analysis, Bäcklund Transformations, and Interaction Solutions for an AB Modified KdV System
An AB modified KdV (AB-mKdV) system which can be used to describe two-place event is studied in this manuscript. Because the AB-mKdV system is considered as a special reduction of the famous AKNS system, the properties of the AKNS system are first revealed by using symmetry analysis. The nonlocal sy...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/4652126 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849401033137061888 |
|---|---|
| author | Man Jia |
| author_facet | Man Jia |
| author_sort | Man Jia |
| collection | DOAJ |
| description | An AB modified KdV (AB-mKdV) system which can be used to describe two-place event is studied in this manuscript. Because the AB-mKdV system is considered as a special reduction of the famous AKNS system, the properties of the AKNS system are first revealed by using symmetry analysis. The nonlocal symmetries related to truncated Painlevé expansion, the finite transformation, and the symmetry reduction solutions of the AKNS system are presented. The corresponding Bäcklund transformations and the interaction solutions of the AB-mKdV system are constructed based on the special reduction. The results demonstrate that the AB-mKdV system possesses many kinds of interaction solutions, such as the interactions between kink and soliton and kink and cnoidal waves. The soliton can be changed from bright to dark during propagation. |
| format | Article |
| id | doaj-art-8a15c7a79ca74b0fa23e8859488e1647 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-8a15c7a79ca74b0fa23e8859488e16472025-08-20T03:37:51ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/46521264652126Symmetry Analysis, Bäcklund Transformations, and Interaction Solutions for an AB Modified KdV SystemMan Jia0Laboratory of Clean Energy Storage and Conversion, School of Physical Science and Technology, Ningbo University, Ningbo 315211, ChinaAn AB modified KdV (AB-mKdV) system which can be used to describe two-place event is studied in this manuscript. Because the AB-mKdV system is considered as a special reduction of the famous AKNS system, the properties of the AKNS system are first revealed by using symmetry analysis. The nonlocal symmetries related to truncated Painlevé expansion, the finite transformation, and the symmetry reduction solutions of the AKNS system are presented. The corresponding Bäcklund transformations and the interaction solutions of the AB-mKdV system are constructed based on the special reduction. The results demonstrate that the AB-mKdV system possesses many kinds of interaction solutions, such as the interactions between kink and soliton and kink and cnoidal waves. The soliton can be changed from bright to dark during propagation.http://dx.doi.org/10.1155/2020/4652126 |
| spellingShingle | Man Jia Symmetry Analysis, Bäcklund Transformations, and Interaction Solutions for an AB Modified KdV System Advances in Mathematical Physics |
| title | Symmetry Analysis, Bäcklund Transformations, and Interaction Solutions for an AB Modified KdV System |
| title_full | Symmetry Analysis, Bäcklund Transformations, and Interaction Solutions for an AB Modified KdV System |
| title_fullStr | Symmetry Analysis, Bäcklund Transformations, and Interaction Solutions for an AB Modified KdV System |
| title_full_unstemmed | Symmetry Analysis, Bäcklund Transformations, and Interaction Solutions for an AB Modified KdV System |
| title_short | Symmetry Analysis, Bäcklund Transformations, and Interaction Solutions for an AB Modified KdV System |
| title_sort | symmetry analysis backlund transformations and interaction solutions for an ab modified kdv system |
| url | http://dx.doi.org/10.1155/2020/4652126 |
| work_keys_str_mv | AT manjia symmetryanalysisbacklundtransformationsandinteractionsolutionsforanabmodifiedkdvsystem |