Generalized Matrix Exponential Solutions to the AKNS Hierarchy

Generalized matrix exponential solutions to the AKNS equation are obtained by the inverse scattering transformation (IST). The resulting solutions involve six matrices, which satisfy the coupled Sylvester equations. Several kinds of explicit solutions including soliton, complexiton, and Matveev solu...

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Main Authors: Jian-bing Zhang, Canyuan Gu, Wen-Xiu Ma
Format: Article
Language:English
Published: Wiley 2018-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2018/1375653
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author Jian-bing Zhang
Canyuan Gu
Wen-Xiu Ma
author_facet Jian-bing Zhang
Canyuan Gu
Wen-Xiu Ma
author_sort Jian-bing Zhang
collection DOAJ
description Generalized matrix exponential solutions to the AKNS equation are obtained by the inverse scattering transformation (IST). The resulting solutions involve six matrices, which satisfy the coupled Sylvester equations. Several kinds of explicit solutions including soliton, complexiton, and Matveev solutions are deduced from the generalized matrix exponential solutions by choosing different kinds of the six involved matrices. Generalized matrix exponential solutions to a general integrable equation of the AKNS hierarchy are also derived. It is shown that the general equation and its matrix exponential solutions share the same linear structure.
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publishDate 2018-01-01
publisher Wiley
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spelling doaj-art-422d6af8fce747b5a5b83b8a22a39a982025-08-20T02:37:51ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/13756531375653Generalized Matrix Exponential Solutions to the AKNS HierarchyJian-bing Zhang0Canyuan Gu1Wen-Xiu Ma2School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, ChinaSchool of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, ChinaDepartment of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USAGeneralized matrix exponential solutions to the AKNS equation are obtained by the inverse scattering transformation (IST). The resulting solutions involve six matrices, which satisfy the coupled Sylvester equations. Several kinds of explicit solutions including soliton, complexiton, and Matveev solutions are deduced from the generalized matrix exponential solutions by choosing different kinds of the six involved matrices. Generalized matrix exponential solutions to a general integrable equation of the AKNS hierarchy are also derived. It is shown that the general equation and its matrix exponential solutions share the same linear structure.http://dx.doi.org/10.1155/2018/1375653
spellingShingle Jian-bing Zhang
Canyuan Gu
Wen-Xiu Ma
Generalized Matrix Exponential Solutions to the AKNS Hierarchy
Advances in Mathematical Physics
title Generalized Matrix Exponential Solutions to the AKNS Hierarchy
title_full Generalized Matrix Exponential Solutions to the AKNS Hierarchy
title_fullStr Generalized Matrix Exponential Solutions to the AKNS Hierarchy
title_full_unstemmed Generalized Matrix Exponential Solutions to the AKNS Hierarchy
title_short Generalized Matrix Exponential Solutions to the AKNS Hierarchy
title_sort generalized matrix exponential solutions to the akns hierarchy
url http://dx.doi.org/10.1155/2018/1375653
work_keys_str_mv AT jianbingzhang generalizedmatrixexponentialsolutionstotheaknshierarchy
AT canyuangu generalizedmatrixexponentialsolutionstotheaknshierarchy
AT wenxiuma generalizedmatrixexponentialsolutionstotheaknshierarchy