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...

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Main Author: Man Jia
Format: Article
Language:English
Published: Wiley 2020-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2020/4652126
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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
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institution Kabale University
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publishDate 2020-01-01
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record_format Article
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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