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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Bibliographic Details
Published inAdvances in Mathematical Physics Vol. 2018; no. 2018; pp. 1 - 9
Main Authors Zhang, Jian-bing, Ma, Wen-Xiu, Gu, Canyuan
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2018
Hindawi
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Applied mathematics
Control theory
Differential equations, Nonlinear
Inverse scattering
Mathematical analysis
Matrices
Matrix methods
Physics
Science
Solitons
United States
China
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Summary: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.
ISSN:1687-9120
1687-9139
DOI:10.1155/2018/1375653