Polynomial 𝜏-functions for the AKNS hierarchy

1989 ◽  
pp. 133-141 ◽  
Author(s):  
Robert L. Sachs
Keyword(s):  
Akns Hierarchy

scholarly journals Generalized Matrix Exponential Solutions to the AKNS Hierarchy

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Jian-bing Zhang ◽  
Canyuan Gu ◽  
Wen-Xiu Ma
Keyword(s):  
Inverse Scattering ◽  
General Equation ◽  
Linear Structure ◽  
Integrable Equation ◽  
Matrix Exponential ◽  
Explicit Solutions ◽  
Akns Hierarchy ◽  
Generalized Matrix ◽  
Akns Equation ◽  
Matveev Solutions

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.

scholarly journals The Strict AKNS Hierarchy: Its Structure and Solutions

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
G. F. Helminck
Keyword(s):  
Commutative Algebra ◽  
Loop Space ◽  
Integrable Hierarchy ◽  
Akns Hierarchy ◽  
Zero Curvature ◽  
Lax Equations

We discuss an integrable hierarchy of compatible Lax equations that is obtained by a wider deformation of a commutative algebra in the loop space ofsl2than that in the AKNS case and whose Lax equations are based on a different decomposition of this loop space. We show the compatibility of these Lax equations and that they are equivalent to a set of zero curvature relations. We present a linearization of the system and conclude by giving a wide construction of solutions of this hierarchy.

Riemann–Hilbert problems of a nonlocal reverse-time six-component AKNS system of fourth order and its exact soliton solutions

2021 ◽  
pp. 2150035
Author(s):  
Alle Adjiri ◽  
Ahmed M. G. Ahmed ◽  
Wen-Xiu Ma
Keyword(s):  
Fourth Order ◽  
Soliton Solutions ◽  
Reverse Time ◽  
Akns Hierarchy ◽  
Spectral Problems ◽  
Jump Matrix ◽  
Akns System ◽  
Associated Matrix ◽  
Time Reduction ◽  
Exact Soliton Solutions

We investigate the solvability of an integrable nonlinear nonlocal reverse-time six-component fourth-order AKNS system generated from a reduced coupled AKNS hierarchy under a reverse-time reduction. Riemann–Hilbert problems will be formulated by using the associated matrix spectral problems, and exact soliton solutions will be derived from the reflectionless case corresponding to an identity jump matrix.

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